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• 1. Ackelh, A.S.
Institute for Complex Molecular Systems & Centre for Analysis, Scientific computing and Applications, Eindhoven University of Technology.
Preface to "modeling with measures"2015In: Mathematical Biosciences and Engineering, ISSN 1547-1063, E-ISSN 1551-0018, Vol. 12, no 2Article in journal (Refereed)
• 2.
Japan Womens Univ, Fac Sci, Dept Math, Bunkyo Ku, Tokyo.
Vrije Univ Amsterdam, Fac Sci, Dept Math, Amsterdam, Netherlands. Bukkyo Univ, Sch Educ Math, Kita Ku, Kyoto. Eindhoven Univ Technol, Dept Math & Comp Sci,.
Analysis of non-equilibrium evolution problems: Selected topics in material and life sciences2014In: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179, Vol. 7, no 1Article in journal (Refereed)
• 3. Aiki, T.
Eindhoven Univ Technol, Dept Math & Comp Sci.
A free-boundary problem for concrete carbonation: Front nucleation and rigorous justification of the root t-law of propagation2013In: Interfaces and free boundaries (Print), ISSN 1463-9963, E-ISSN 1463-9971, Vol. 15, no 2, p. 167-180Article in journal (Refereed)
• 4. Aiki, T.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Existence and uniqueness of solutions to a mathematical model predicting service life of concrete structures2009In: Advances in Mathematical Sciences and Applications, ISSN 1343-4373, Vol. 19, p. 119-129Article in journal (Refereed)
• 5.
Gifu University, Japan.
Eindhoven University Technology, Netherlands. Eindhoven University Technology, Netherlands.
On a one-dimensional shape-memory alloy model in its fast-temperature- activation limit2012In: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179, Vol. 5, no 1, p. 15-28Article in journal (Refereed)
• 6.
Gifu University, Japan.
Eindhoven University of Technology.
Large time behavior of solutions to a moving-interface problem modeling concrete carbonation2010In: Communications on Pure and Applied Analysis, ISSN 1534-0392, E-ISSN 1553-5258, Vol. 9, no 5, p. 1117-1129Article in journal (Refereed)
• 7.
Tokyo Womens University.
Netherlands.
Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry’s law and time-dependent Dirichlet data2013In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 93, p. 3-14Article in journal (Refereed)

We study the large-time behavior of the free boundary position capturing the one-dimensional motion of the carbonation reaction front in concrete-based materials. We extend here our rigorous justification of the t-behavior of reaction penetration depths by including nonlinear effects due to deviations from the classical Henry's law and time-dependent Dirichlet data.

• 8. Aiki, Toyohiko
Eindhoven University of Technology.
Large-time behavior of a two-scale semilinear reaction-diffusion system for concrete sulfatation2014In: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476, Vol. 38, no 7, p. 1451-1464Article in journal (Refereed)
• 9.
Gifu University, Japan.
Eindhoven University of Technology.
On uniqueness of a weak solution of one-dimensional concrete carbonation problem2011In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 29, no 4, p. 1345-1365Article in journal (Refereed)

In our previous works we studied a one-dimensional free-boundary model related to the aggressive penetration of gaseous carbon dioxide in unsaturated concrete. Essentially, global existence and uniqueness of weak solutions to the model were obtained when the initial functions are bounded on the domain. In this paper we investigate the well-posedness of the problem for the case when the initial functions belong to a $\displaystyle{{L}}^{{2}}-$ class. Specifically, the uniqueness of weak solutions is proved by applying the dual equation method.

• 10.
All Russia Res Inst Automat VNIIA, Moscow, Russia.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science. All Russia Res Inst Automat VNIIA, Moscow, Russia.;RAS, PN Lebedev Phys Inst, Moscow 117901, Russia. All Russia Res Inst Automat VNIIA, Moscow, Russia.;RAS, PN Lebedev Phys Inst, Moscow 117901, Russia. All Russia Res Inst Automat VNIIA, Moscow, Russia. RAS, MV Keldysh Appl Math Inst, Moscow 117901, Russia.
Stochastic simulation of the nonlinear kinetic equation with high-frequency electromagnetic fields2013In: PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY, ISSN 1562-6016, no 4, p. 233-237Article in journal (Refereed)

A general approach to Monte Carlo methods for Coulomb collisions is proposed. Its key idea is an approximation of Landau-Fokker-Planck (LFP) equations by Boltzmann equations of quasi-Maxwellian kind. High-frequency fields are included into consideration and comparison with the well-known results are given.

• 11.
Karlstad University, Faculty of Technology and Science, Department of Mathematics.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
A new variational characterization of Sobolev spaces2015In: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 25, no 4, p. 2185-2195Article in journal (Refereed)

We obtain a new variational characterization of the Sobolev space $W_p^1(\Omega)$ (where $\Omega\subseteq\R^n$ and $p>n$). This is a generalization of a classical result of F. Riesz. We also consider some related results.

• 12.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Romania. Department of Mathematics and Computer Science, Technical University of Civil Engineering Bucharest, Romania.
Factorizations of Weighted Hardy Inequalities2018In: Bulletin of the Brazilian Mathematical Society, ISSN 1678-7544, E-ISSN 1678-7714, p. 1-18Article in journal (Refereed)
• 13.
Karlstad University, Faculty of Health, Science and Technology (starting 2013).
Karlstad University, Faculty of Health, Science and Technology (starting 2013). Stockholm University. Stockholm University. Stockholm University.
Growth Histories in Bimetric Massive Gravity2012In: Journal of Cosmology and Astroparticle Physics, ISSN 1475-7516, E-ISSN 1475-7516, no 12, article id 021Article in journal (Refereed)

We perform cosmological perturbation theory in Hassan-Rosen bimetric gravity for general homogeneous and isotropic backgrounds. In the de Sitter approximation, we obtain decoupled sets of massless and massive scalar gravitational fluctuations. Matter perturbations then evolve like in Einstein gravity. We perturb the future de Sitter regime by the ratio of matter to dark energy, producing quasi-de Sitter space. In this more general setting the massive and massless fluctuations mix. We argue that in the quasi-de Sitter regime, the growth of structure in bimetric gravity differs from that of Einstein gravity.

• 14.
Karlstad University, Division for Engineering Sciences, Physics and Mathematics.
Baire category theorem2009Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

In this thesis we give an exposition of the notion of category and the Baire category theorem as a set theoretical method for proving existence. The category method was introduced by René Baire to describe the functions that can be represented by a limit of a sequence of continuous real functions. Baire used the term functions of the first class to denote these functions.

The usage of the Baire category theorem and the category method will be illustrated by some of its numerous applications in real and functional analysis. Since the usefulness, and generality, of the category method becomes fully apparent in Banach spaces, the applications provided have been restricted to these spaces.

To some extent, basic concepts of metric topology will be revised, as the Baire category theorem is formulated and proved by these concepts. In addition to the Baire category theorem, we will give proof of equivalence between different versions of the theorem.

Explicit examples, of first class functions will be presented, and we shall state a theorem, due to Baire, providing a necessary condition on the set of points of continuity for any function of the first class.

• 15.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
Discrete Velocity Models for Polyatomic Molecules Without Nonphysical Collision Invariants2018In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 172, no 3, p. 742-761Article in journal (Refereed)

An important aspect of constructing discrete velocity models (DVMs) for the Boltzmann equation is to obtain the right number of collision invariants. Unlike for the Boltzmann equation, for DVMs there can appear extra collision invariants, so called spurious collision invariants, in plus to the physical ones. A DVM with only physical collision invariants, and hence, without spurious ones, is called normal. The construction of such normal DVMs has been studied a lot in the literature for single species, but also for binary mixtures and recently extensively for multicomponent mixtures. In this paper, we address ways of constructing normal DVMs for polyatomic molecules (here represented by that each molecule has an internal energy, to account for non-translational energies, which can change during collisions), under the assumption that the set of allowed internal energies are finite. We present general algorithms for constructing such models, but we also give concrete examples of such constructions. This approach can also be combined with similar constructions of multicomponent mixtures to obtain multicomponent mixtures with polyatomic molecules, which is also briefly outlined. Then also, chemical reactions can be added.

• 16.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
Half-Space Problems for a Linearized Discrete Quantum Kinetic Equation2015In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 159, no 2, p. 358-379Article in journal (Refereed)

We study typical half-space problems of rarefied gas dynamics, including the problems of Milne and Kramer, for a general discrete model of a quantum kinetic equation for excitations in a Bose gas. In the discrete case the plane stationary quantum kinetic equation reduces to a system of ordinary differential equations. These systems are studied close to equilibrium and are proved to have the same structure as corresponding systems for the discrete Boltzmann equation. Then a classification of well-posed half-space problems for the homogeneous, as well as the inhomogeneous, linearized discrete kinetic equation can be made. The number of additional conditions that need to be imposed for well-posedness is given by some characteristic numbers. These characteristic numbers are calculated for discrete models axially symmetric with respect to the x-axis. When the characteristic numbers change is found in the discrete as well as the continuous case. As an illustration explicit solutions are found for a small-sized model.

• 17.
Univ Glasgow, Sch Math & Stat, Glasgow.
Eindhoven Univ Technol, Dept Math & Comp Sci, NL. Eindhoven Univ Technol, Dept Math & Comp Sci, NL. Eindhoven University of Technology,.
Is adding charcoal to soil a good method for CO2 sequestration? -: Modeling a spatially homogeneous soil2014In: Applied Mathematical Modelling, ISSN 0307-904X, E-ISSN 1872-8480, Vol. 38, no 9-10, p. 2463-2475Article in journal (Refereed)
• 18.
University of Bremen.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
Corrector estimates for the homogenization of a two-scale thermoelasticity problem with a priori known phase transformations2017In: Electronic Journal of Differential Equations, ISSN 1550-6150, E-ISSN 1072-6691, no 57, p. 1-21Article in journal (Refereed)

We investigate corrector estimates for the solutions of a thermoelasticity problem posed in a highly heterogeneous two-phase medium and its corresponding two-scale thermoelasticity model which was derived in [11] by two-scale convergence arguments. The medium in question consists of a connected matrix with disconnected, initially periodically distributed inclusions separated by a sharp interface undergoing a priori known phase transformations. While such estimates seem not to be obtainable in the fully coupled setting, we show that for some simplified scenarios optimal convergence rates can be proven rigorously. The main technique for the proofs are energy estimates using special reconstructions of two-scale functions and particular operator estimates for periodic functions with zero average. Here, additional regularity results for the involved functions are necessary.

• 19.
Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England.
Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England. Eindhoven University of Technology.
Single and two-scale sharp-interface models for concrete carbonation - Asymptotics and numerical approximation2012In: Multiscale Modeling & simulation, ISSN 1540-3459, E-ISSN 1540-3467, Vol. 10, no 3, p. 874-905Article in journal (Refereed)
• 20.
Eindhoven University of Technology.
Leiden University. Eindhoven University of Technology.
Modelling with measures: Approximation of a mass-emitting object by a point source2015In: Mathematical Biosciences and Engineering, ISSN 1547-1063, E-ISSN 1551-0018, Mathematical Biosciences and Engineering, Vol. 12, no 2, p. 357-373Article in journal (Refereed)
• 21.
Netherlands.
Netherlands. Eindhoven University of Technology, The Netherlands.
Well-posedness and approximation of a measure-valued mass evolution problem with flux boundary conditions2014In: Comptes rendus. Mathematique, ISSN 1631-073X, E-ISSN 1778-3569, Vol. 352, no 1, p. 51-54Article in journal (Refereed)

This Note deals with imposing a flux boundary condition on a non-conservative measure-valued mass evolution problem posed on a bounded interval. To establish the wellposedness of the problem, we exploit particle system approximations of the mass accumulation in a thin layer near the active boundary. We derive the convergence rate for the approximation procedure as well as the structure of the flux boundary condition in the limit problem.

• 22.
Eindhoven University of Technology, Netherlands.
Leiden University, Netherlands. Eindhoven University of Technology, Netherlands.
Mild solutions to a measure-valued mass evolution problem with flux boundary conditions2015In: Journal of Differential Equations, ISSN 0022-0396, E-ISSN 1090-2732, Vol. 259, no 3, p. 1068-1097Article in journal (Refereed)

We investigate the well-posedness and approximation of mild solutions to a class of linear transport equations on the unit interval [0, 1] endowed with a linear discontinuous production term, formulated in the space M([0, 1]) of finite Borel measures. Our working technique includes a detailed boundary layer analysis in terms of a semigroup representation of solutions in spaces of measures able to cope with the passage to the singular limit where thickness of the layer vanishes. We obtain not only a suitable concept of solutions to the chosen measure-valued evolution problem, but also derive convergence rates for the approximation procedure and get insight in the structure of flux boundary conditions for the limit problem.

• 23.
Eindhoven University of Technology, Netherlands.
Meiji University, Tokyo. Meiji University, Tokyo. Eindhoven University of Technology, Netherlands.
Homogenization and dimension reduction of filtration combustion in heterogeneous thin layers2014In: Networks and Heterogeneous Media, ISSN 1556-1801, E-ISSN 1556-181X, Vol. 9, no 4, p. 709-737Article in journal (Refereed)

We study the homogenization of a reaction-diffusion-convection system posed in an epsilon-periodic delta-thin layer made of a two-component (solid-air) composite material. The microscopic system includes heat flow, diffusion and convection coupled with a nonlinear surface chemical reaction. We treat two distinct asymptotic scenarios: (1) For a fixed width delta > 0 of the thin layer, we homogenize the presence of the microstructures (the classical periodic homogenization limit epsilon --> 0); (2) In the homogenized problem, we pass to delta --> 0 (the vanishing limit of the layer's width). In this way, we are preparing the stage for the simultaneous homogenization (epsilon --> 0) and dimension reduction limit (delta --> 0) with delta = delta (epsilon). We recover the reduced macroscopic equations from [25] with precise formulas for the effective transport and reaction coefficients. We complement the analytical results with a few simulations of a case study in smoldering combustion. The chosen multiscale scenario is relevant for a large variety of practical applications ranging from the forecast of the response to fire of refractory concrete, the microstructure design of resistance-to-heat ceramic-based materials for engines, to the smoldering combustion of thin porous samples under microgravity conditions.

• 24. Fatima, Tasnim
Technical University Eindhoven.
Sulfate attack in sewer pipes: Derivation of a concrete corrosion model via two-scale convergence2014In: Nonlinear Analysis, ISSN 1468-1218, Vol. 15, no 1, p. 326-344Article in journal (Refereed)

We explore the homogenization limit and rigorously derive upscaled equations for a microscopic reaction-diffusion system modeling sulfate corrosion in sewer pipes made of concrete. The system, defined in a periodically-perforated domain, is semi-linear, partially dissipative and weakly coupled via a non-linear ordinary differential equation posed on the solid-water interface at the pore level. First, we show the well-posedness of the microscopic model. We then apply homogenization techniques based on two-scale convergence for a uniformly periodic domain and derive upscaled equations together with explicit formulas for the effective diffusion coefficients and reaction constants. We use a boundary unfolding method to pass to the homogenization limit in the non-linear ordinary differential equation. Finally, we give the strong formulation of the upscaled system.

• 25.
Eindhoven University of Technology.
Eindhoven University of Technology. Gifu University Yanagido.
Distributed space scales in a semilinear reaction-diffusion system including parabolic variational inequality: a well-posedness study2012In: Advances in Mathematical Sciences and Applications, ISSN 1343-4373, Vol. 22, p. 295-318Article in journal (Refereed)
• 26.
Eindhoven Univ Technol, Ctr Anal Sci Comp & Applicat, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands.
Eindhoven University of Technology. Univ Dundee, Div Math, Dundee DD1 4HN, Scotland.
Unfolding-based corrector estimates for a reaction-diffusion system predicting concrete corrosion2012In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 91, no 6, p. 1129-1154Article in journal (Refereed)
• 27.
Technical University Eindhoven, The Netherlands.
Technical University Eindhoven, The Netherlands. Computing Centre of the Russian Academy of Sciences, Moscow, Russia. Technical University Eindhoven, The Netherlands.
Homogenization of a reaction-diffusion system modeling sulfate corrosion of concrete in locally periodic perforated domains2011In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 69, no 2, p. 261-276Article in journal (Refereed)
• 28.
Czech Acad Sci, Inst Math, Prague, Czech Republic.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Univ Freiburg, Inst Math. Charles Univ Prague, Czech republic. Czech Tech Univ; Univ South Bohemia, Czech republic.
Embeddings of Lorentz-type spaces involving weighted integral means2017In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 273, no 9, p. 2939-2980Article in journal (Refereed)

We solve the problem of characterizing weights on (0, infinity) for which the inequality involving two possibly different general inner weighted means (integral(infinity)(0)(integral(t)(0)f*(s)(m2)u(2)(s)ds)(p2/m2) w(2)(t)dt)(1/p2) <= C(integral(infinity)(0)(integral(t)(0)f*(s)(m2)u(1)(s)ds)(p1/m1) w(1)(t)dt)(1/p1) holds, where p(1), p(2), m(1), m(2) is an element of (0, infinity) and p(2) > m(2). The proof is based on a new approach combining duality techniques with sharp weighted estimates for iterated integral and supremum operators. (C) 2017 Elsevier Inc. All rights reserved.

• 29.
Karlstad University, Faculty of Health, Science and Technology (starting 2013).
Kan elever utveckla sin taluppfattning vid användandet av digitala spel?: En innehållsanalys av digitala spel med fokus på området taluppfattning2017Independent thesis Advanced level (degree of Master (One Year)), 20 credits / 30 HE creditsStudent thesis

The purpose of this study was to examine if digital games made for entertainment can offer the player skill training in the area of number sense in mathematics. The study took place on 11 games chosen after talking to student in class 4–6 and the framework was based on McIntosh interputation of number sense and six aspects was created. A coding scheme was used to examine if the games included situations where number sense could be used and how the player could practice their number sense in these situations. The study shows that the possibilities for practice is in the games but some games differentiate from others by offering the player more complex calculating situations than the other games. The aspect of multiple representations for numbers was separated from the others because all analyzed situations did not contain this aspect. The result of the study shows that teachers can use these games and themselves analyze other games to use in mathematic learning situations.

• 30.
Karlstad University, Faculty of Technology and Science.
CAP KC3-12: Design and finite element analysis2007Independent thesis Basic level (professional degree), 20 credits / 30 HE creditsStudent thesis

In offshore oil production FMC Subsea systems use a product called cap. The cap´s mainly task is to protect hubface and seal areas on inboard hub against dirt, corrosion and mechanical damage under installation of a subsea system. A new model of a cap has been designed and analysed using finite element method. The model is called KC3-12 and has a new function, emergency release, which is a backup method for the ROV (remote operated vehicle) to release the cap from the hubface when it is placed under water. The cap KC3-12 was found to fulfil the criteria under the test load pressure, according to ASME VIII, div2. The analysis shows that a higher pressure can be allowed on the cap since the collapse load occurs at 7.2 times test pressure and 1.2 times test pressure is allowed.

• 31.
Meiji University,Tokyo, Japan.
Eindhoven University of Technology. Meiji University, Tokyo, Japan.
Pattern formation in reverse smouldering combustion: A homogenisation approach2013In: Combustion theory and modelling, ISSN 1364-7830, E-ISSN 1741-3559, Vol. 17, no 2, p. 185-223Article in journal (Refereed)

The development of fingering char patterns on the surface of porous thin materials has been investigated in the framework of reverse combustion. This macroscopic characteristic feature of combustible media has also been studied experimentally and through the use of phenomenological models. However, not much attention has been given to the behaviour of the emerging patterns based on characteristic material properties. Starting from a microscopic description of the combustion process, macroscopic models of reverse combustion that are derived by the application of the homogenisation technique are presented. Using proper scaling by means of a small scale parameter E, the results of the formal asymptotic procedure are justified by qualitative multiscale numerical simulations at the microscopic and macroscopic levels. We consider two equilibrium models that are based on effective conductivity contrasts, in a simple adiabatic situation, to investigate the formation of unstable fingering patterns on the surface of a charred material. The behaviour of the emerging patterns is analysed using primarily the Peclet and Lewis numbers as control parameters.

• 32.
Karlstad University, Faculty of Technology and Science, Department of Mathematics.
Iterated rearrangements and Gagliardo-Sobolev type inequalities2012In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, Vol. 387, no 1, p. 335-348Article in journal (Refereed)

In this paper we consider Lorentz type spaces defined in terms of iterated rearrangements of functions of several variables (σ is a permutation of {1,…,n}). Further, we study Fournier–Gagliardo mixed norm spaces V(Rn) closely related to Sobolev spaces . We prove estimate of via ‖fV with the sharp constant. In particular, this gives a refinement of the known Sobolev type inequalities for the space .

• 33.
Karlstad University, Faculty of Technology and Science, Department of Mathematics.
On Fubini type property in Lorentz spaces2012In: Recent Advances in Harmonic Analysis and Applications / [ed] Bilyk, D., New York: Springer, 2012, p. 171-179Chapter in book (Refereed)

We study Fubini-type property for Lorentz spaces L p,r (R 2 ) . This problem is twofold. First we assume that all linear sections of a function f in directions of coordinate axes belong to L p,r (R) , and their one-dimensional Lp, r-norms belong to L p,r (R). We show that for pr it does not imply that f∈L p,r (R 2 ) (this complements one result by Cwikel). Conversely, we assume that f∈L p,r (R 2 ) , and we show that then for r < p almost all linear sections of f belong to L p,r (R) , but for p < r all linear sections may have infinite one-dimensional Lp, r-norms

• 34.
Karlstad University, Faculty of Technology and Science, Department of Mathematics.
Karlstad University, Faculty of Technology and Science, Department of Mathematics.
On functions of bounded p-variation2009In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 356, no 2, p. 582-604Article in journal (Refereed)

We obtain estimates of the total p-variation (1<p<∞) and other related functionals for a periodic function fLp[0,1] in terms of its Lp-modulus of continuity ωp(f;δ). These estimates are sharp for any rate of the decay of ωp(f;δ). Moreover, the constant coefficients in them depend on parameters in an optimal way.

• 35.
Karlstad University, Faculty of Technology and Science, Department of Mathematics.
Karlstad University, Faculty of Technology and Science, Department of Mathematics.
On moduli of p-continuity2012In: Acta Mathematica Hungarica, ISSN 0236-5294, E-ISSN 1588-2632, Vol. 137, no 3, p. 191-213Article in journal (Refereed)

Moduli of p-continuity provide a measure of fractional smoothness of functions via p-variation. We prove sharp estimates of the modulus of p-continuty in terms of the modulus of q-continuity (1<p<q<\infty).

• 36.
Eindhoven University of Technology, Netherlands.
Japan Women's University, Japan. Eindhoven University of Technology, Netherlands.
Homogenization of a thermo-diffusion system with smoluchowski interactions2014In: Networks and Heterogeneous Media, ISSN 1556-1801, E-ISSN 1556-181X, Vol. 9, no 4, p. 739-762Article in journal (Refereed)

We study the solvability and homogenization of a thermal-diffusion reaction problem posed in a periodically perforated domain. The system describes the motion of populations of hot colloidal particles interacting together via Smoluchowski production terms. The upscaled system, obtained via two-scale convergence techniques, allows the investigation of deposition effects in porous materials in the presence of thermal gradients.

• 37.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Bilinear weighted Hardy inequality for nonincreasing functions2017In: Publications mathématiques (Bures-sur-Yvette), ISSN 0073-8301, E-ISSN 1618-1913, Vol. 61, no 1, p. 3-50Article in journal (Refereed)
• 38.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Charles University in Prague, Department of Mathematical Analysis.
Boundedness of Hardy-type operators with a kernel: integral weighted conditions for the case $0<q<1\le p<\infty$2017In: Revista Matemática Complutense, ISSN 1139-1138, E-ISSN 1988-2807, Vol. 30, no 3, p. 547-587Article in journal (Refereed)

Boundedness of a fundamental Hardy-type operator with a kernel is characterized between weighted Lebesgue spaces $L^p(v)$ and $L^q(w)$ for $0<q<1\le p<\infty$. The conditions are explicit and have a standard integral form.

• 39.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Convolution in weighted Lorentz spaces of type Γ2016In: Mathematica Scandinavica, ISSN 0025-5521, E-ISSN 1903-1807, Vol. 119, no 1, p. 113-132Article in journal (Refereed)
• 40.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Convolution inequalities in weighted Lorentz spaces2014In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 17, no 4, p. 1201-1223Article in journal (Refereed)

We characterize boundedness of a convolution operator with a fixed kernel between the weighted Lorentz spaces Lambda(p)(v) and Gamma(q)(w) for 0 < p <= q <= infinity, 1 <= q < p < infinity and 0 < q <= p = infinity. We provide corresponding weighted Young-type inequalities and also study basic properties of some new involved r.i. spaces.

• 41.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013). Charles University in Prague, Department of Mathematical Analysis.
Convolution inequalities in weighted Lorentz spaces: case 0<q<12017In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 20, no 1, p. 191-201Article in journal (Refereed)

We characterize boundedness of a convolution operator between weighted Lorentz spaces $\Lambda^p(v)$and $\Gamma^q(w)$ in the case $0<q<1$.

• 42.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Forever Young: Convolution Inequalities in Weighted Lorentz-type Spaces2014Licentiate thesis, comprehensive summary (Other academic)

This thesis is devoted to an investigation of boundedness of a general convolution operator between certain weighted Lorentz-type spaces with the aim of proving analogues of the Young convolution inequality for these spaces.

Necessary and sufficient conditions on the kernel function are given, for which the convolution operator with the fixed kernel is bounded between a certain domain space and the weighted Lorentz space of type Gamma. The considered domain spaces are the weighted Lorentz-type spaces defined in terms of the nondecreasing rearrangement of a function, the maximal function or the difference of these two quantities.

In each case of the domain space, the corresponding Young-type convolution inequality is proved and the optimality of involved rearrangement-invariant spaces in shown.

Furthermore, covering of the previously existing results is also discussed and some properties of the new rearrangement-invariant function spaces obtained during the process are studied.

• 43.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Integral conditions for Hardy-type operators involving suprema2017In: Collectanea Mathematica (Universitat de Barcelona), ISSN 0010-0757, E-ISSN 2038-4815, Vol. 68, no 1, p. 21-50Article in journal (Refereed)

The article contains characterizations of boundedness of an iterated supremal Hardy-type operator between weighted Lebesgue spaces, and an supremal Hardy operator restricted to positive decreasing functions between the same spaces. The found condtitions have an explicit integral/supremal form and cover all possible cases of positive exponents of the involved spaces.

• 44.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science. Charles University in Prague, Department of Mathematical Analysis.
Iterating bilinear Hardy inequalities2017In: Proceedings of the Edinburgh Mathematical Society, ISSN 0013-0915, E-ISSN 1464-3839Article in journal (Refereed)

An iteration technique to characterize boundedness of certain types of multilinear operators is presented, reducing the problem into a corresponding linear-operator case. The method gives a simple proof of a characterization of validity of a bilinear Hardy inequality in the weighted Lebesgue space setting. More equivalent characterizing conditions are presented. The same technique is applied to various further problems, in particular those involving multilinear integral operators of Hardy type.

• 45.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
The Weighted Space Odyssey2017Doctoral thesis, comprehensive summary (Other academic)

The common topic of this thesis is boundedness of integral and supremal operators between weighted function spaces.

The first type of results are characterizations of boundedness of a convolution-type operator between general weighted Lorentz spaces. Weighted Young-type convolution inequalities are obtained and an optimality property of involved domain spaces is proved. Additional provided information includes an overview of basic properties of some new function spaces appearing in the proven inequalities.

In the next part, product-based bilinear and multilinear Hardy-type operators are investigated. It is characterized when a bilinear Hardy operator inequality holds either for all nonnegative or all nonnegative and nonincreasing functions on the real semiaxis. The proof technique is based on a reduction of the bilinear problems to linear ones to which known weighted inequalities are applicable.

Further objects of study are iterated supremal and integral Hardy operators, a basic Hardy operator with a kernel and applications of these to more complicated weighted problems and embeddings of generalized Lorentz spaces. Several open problems related to missing cases of parameters are solved, thus completing the theory of the involved fundamental Hardy-type operators.

• 46.
Karlstad University, Faculty of Technology and Science, Department of Mathematics.
Estimates of the total p-variation of bivariate functions2013In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 401, p. 218-231Article in journal (Refereed)

We obtain sharp estimates of the Hardy-Vitali type p-variation of a function of two variables in terms of its mixed modulus of continuity in Lp([0,1]2).

• 47.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Fubini-type properties of bivariate functions of bounded ρ-variation2014In: Acta Scientarum Mathematicarum, ISSN 0001-6969, Vol. 80, no 4, p. 467-475Article in journal (Refereed)

We investigate Fubini-type properties of the space of functions of bounded Hardy-Vitali-type p-variation. This leads us to consider mixed norm spaces of bivariate functions whose linear sections have bounded p-variation in the sense of Wiener

• 48.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Functions of Generalized Bounded Variation2013Doctoral thesis, monograph (Other academic)

This thesis is devoted to the study of different generalizations of the classical conception of a function of bounded variation.

First, we study the functions of bounded p-variation introduced by Wiener in 1924. We obtain estimates of the total p-variation (1<p<∞) and other related functionals for a periodic function f in Lp([0,1]) in terms of its Lp-modulus of continuity ω(f;δ)p. These estimates are sharp for any rate of decay of ω(f;δ)p. Moreover, the constant coefficients in them depend on parameters in an optimal way.

Inspired by these results, we consider the relationship between the Riesz type generalized variation vp,α(f) (1<p<∞, 0≤α≤1-1/p) and the modulus of p-continuity  ω1-1/p(f;δ). These functionals generate scales of spaces that connect the space of functions of bounded p-variation and the Sobolev space Wp1. We prove sharp estimates of vp,α(f) in terms of ω1-1/p(f;δ).

In the same direction, we study relations between moduli of p-continuity and q-continuity for 1<p<q<. We prove an inequality that estimates ω1-1/p(f;δ) in terms of ω1-1/q(f;δ). The inequality is sharp for any order of decay of ω1-1/q(f;δ).

Next, we study another generalization of bounded variation: the so-called bounded Λ-variation, introduced by Waterman in 1972. We investigate relations between the space ΛBV of functions of bounded Λ-variation, and classes of functions defined via integral smoothness properties. In particular, we obtain the necessary and sufficient condition for the embedding of the class Lip(α;p) into ΛBV. This solves a problem of Wang (2009).

We consider also functions of two variables. Applying our one-dimensional result, we obtain sharp estimates of the Hardy-Vitali type p-variation of a bivariate function in terms of its mixed modulus of continuity in Lp([0,1]2). Further, we investigate Fubini-type properties of the space Hp(2) of functions of bounded Hardy-Vitali p-variation. This leads us to consider the symmetric mixed norm space Vp[Vp]sym of functions of bounded iterated p-variation. For p>1, we prove that Hp(2) is not embedded into Vp[Vp]sym, and that Vp[Vp]sym is not embedded into Hp(2). In other words, Fubini-type properties completely fail in the class of functions of bounded Hardy-Vitali type p-variation for p>1.

• 49.
Karlstad University, Faculty of Technology and Science, Department of Mathematics.
On fractional smoothness of functions related to p-variation2013In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 16, no 1, p. 21-39Article in journal (Refereed)

This paper is concerned with the study of two functionals of variational type - the Riesz type generalized variation v_{p,\alpha}(f) (1<p<\infty, 0\le\alpha\le1-1/p) and the moduli of p-continuity \omega_{1-1/p}(f;d). These functionals generate scales of spaces connecting the class of functions of bounded p-variation and the Sobolev space W_p^1. Some limiting relations in these scales are proved. Sharp estimates of v_{p,\alpha}(f) in terms of \omega_{1-1/p}(f;d) are obtained.

• 50. Meier, Sebastian A.
Technical University of Eindhoven.
A two-scale reaction-diffusion system with micro-cell reaction concentrated on a free boundary2008In: Comptes rendus. Mecanique, ISSN 1631-0721, E-ISSN 1873-7234, Vol. 336, no 6, p. 481-486Article in journal (Refereed)
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