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Lind, M. & Muntean, A. (2018). A Priori Feedback Estimates for Multiscale Reaction-Diffusion Systems. Numerical Functional Analysis and Optimization, 39(4), 413-437
Open this publication in new window or tab >>A Priori Feedback Estimates for Multiscale Reaction-Diffusion Systems
2018 (English)In: Numerical Functional Analysis and Optimization, ISSN 0163-0563, E-ISSN 1532-2467, Vol. 39, no 4, p. 413-437Article in journal (Refereed) Published
Abstract [en]

We study the approximation of a multiscale reaction–diusion system posed on both macroscopic and microscopic space scales. The coupling between the scales is done through micro– macro ux conditions. Our target system has a typical structure for reaction–diusion ow problems in media with distributed microstructures (also called, double porosity materials). Besides ensuring basic estimates for the convergence of two-scale semidiscrete Galerkin approximations, we provide a set of a priori feedback estimates and a local feedback error estimator that help in designing a distributed-high-errors strategy to allow for a computationally ecient zooming in and out from microscopic structures. The error control on the feedback estimates relies on two-scale-energy, regularity, and interpolation estimates as well as on a ne bookeeping of the sources responsible with the propagation of the (multiscale) approximation errors. The working technique based on a priori feedback estimates is in principle applicable to a large class of systems of PDEs with dual structure admitting strong solutions. A

Place, publisher, year, edition, pages
Taylor & Francis, 2018
Keywords
Feedback nite element method, Galerkin approximation, micro–macro coupling, multiscale reaction–diusion systems
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-62808 (URN)10.1080/01630563.2017.1369996 (DOI)
Available from: 2017-08-25 Created: 2017-08-25 Last updated: 2018-05-22Bibliographically approved
Muntean, A. & Seidman, T. I. (2018). Asymptotics of diffusion-limited fast reactions. Quarterly of Applied Mathematics, 76, 199-213
Open this publication in new window or tab >>Asymptotics of diffusion-limited fast reactions
2018 (English)In: Quarterly of Applied Mathematics, ISSN 0033-569X, E-ISSN 1552-4485, Vol. 76, p. 199-213Article in journal (Refereed) Published
Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2018
Keywords
Fast reaction, diffusion, asymptotics
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-47555 (URN)10.1090/qam/1496 (DOI)
Available from: 2016-12-25 Created: 2016-12-25 Last updated: 2018-05-23Bibliographically approved
Gruetzner, S. & Muntean, A. (2018). Brief Introduction to Damage Mechanics and its Relation to Deformations. In: van Meurs, Patrick, Kimura, Masato, Notsu, Hirofumi (Ed.), Mathematical Analysis of Continuum Mechanics and Industrial Applications II: Proceedings of the International Conference CoMFoS16 (pp. 115-124). Springer
Open this publication in new window or tab >>Brief Introduction to Damage Mechanics and its Relation to Deformations
2018 (English)In: Mathematical Analysis of Continuum Mechanics and Industrial Applications II: Proceedings of the International Conference CoMFoS16 / [ed] van Meurs, Patrick, Kimura, Masato, Notsu, Hirofumi, Springer, 2018, p. 115-124Chapter in book (Refereed)
Abstract [en]

We discuss some principle concepts of damage mechanics and outline a possibility to address the open question of the damage-to-deformation relation by suggesting a parameter identification setting. To this end, we introduce a variable motivated by the physical damage phenomenon and comment on its accessibility through measurements. We give an extensive survey on analytic results and present an isotropic irreversible partial damage model in a dynamic mechanical setting in form of a second order hyperbolic equation coupled with an ordinary differential equation for the damage evolution. We end with a note on a possible parameter identification setting.

Place, publisher, year, edition, pages
Springer, 2018
Series
Mathematics for Industry, ISSN ISSN: 2198-350X ; 30
Keywords
damage, mechanics of solids, non-linear differential equations, parameter identification
National Category
Mathematics
Research subject
Materials Engineering; Mathematics
Identifiers
urn:nbn:se:kau:diva-63936 (URN)978-981-10-6283-4 (ISBN)
Available from: 2017-09-24 Created: 2017-09-24 Last updated: 2017-12-08Bibliographically approved
Muntean, A. (2018). Preface. Applicable Analysis, 97(1), 1-2
Open this publication in new window or tab >>Preface
2018 (English)In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 97, no 1, p. 1-2Article in journal (Refereed) Published
Place, publisher, year, edition, pages
Taylor & Francis, 2018
National Category
Natural Sciences Mathematics
Research subject
Mathematics; Mathematics
Identifiers
urn:nbn:se:kau:diva-65303 (URN)10.1080/00036811.2017.1397317 (DOI)
Note

Preface for the Special Issue "Multiscale Inverse Problems"

Available from: 2017-12-01 Created: 2017-12-01 Last updated: 2017-12-04Bibliographically approved
Richardson, O., Jalba, A. & Muntean, A. (2018). The effect of environment knowledge in evacuation scenarios involving fire and smoke: A multiscale modelling and simulation approach. Fire technology
Open this publication in new window or tab >>The effect of environment knowledge in evacuation scenarios involving fire and smoke: A multiscale modelling and simulation approach
2018 (English)In: Fire technology, ISSN 0015-2684, E-ISSN 1572-8099Article in journal (Refereed) Published
National Category
Natural Sciences
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-67503 (URN)
Note

Ej publicerad 2018-06-11 // ÅM

Available from: 2018-06-07 Created: 2018-06-07 Last updated: 2018-06-11
Lind, M., Muntean, A. & Richardson, O. (2018). Well-posedness and inverse Robin estimate for a multiscale elliptic/parabolic system. Applicable Analysis, 97(1), 89-106
Open this publication in new window or tab >>Well-posedness and inverse Robin estimate for a multiscale elliptic/parabolic system
2018 (English)In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 97, no 1, p. 89-106Article in journal (Refereed) Published
Abstract [en]

We establish the well-posedness of a coupled micro–macro parabolic– elliptic system modeling the interplay between two pressures in a gas–liquid mixture close to equilibrium that is filling a porous media with distributed microstructures. Additionally, we prove a local stability estimate for the inverse micro–macro Robin problem, potentially useful in identifying quantitatively a micro–macro interfacial Robin transfer coefficient given microscopic measurements on accessible fixed interfaces. To tackle the solvability issue we use two-scale energy estimates and twoscale regularity/compactness arguments cast in the Schauder’s fixed point theorem. A number of auxiliary problems, regularity, and scaling arguments are used in ensuring the suitable Fréchet differentiability of the solution and the structure of the inverse stability estimate.

Place, publisher, year, edition, pages
Taylor & Francis, 2018
Keywords
Upscaled porous media, two-scale PDE, inverse micro–macro Robin problem
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-62809 (URN)10.1080/00036811.2017.1364366 (DOI)
Available from: 2017-08-25 Created: 2017-08-25 Last updated: 2018-06-12Bibliographically approved
Cirillo, E., Colangeli, M. & Muntean, A. (2017). Trapping in bottlenecks: Interplay between microscopic dynamics and large scale effects. Physica A: Statistical Mechanics and its Applications, 488(11), 30-38
Open this publication in new window or tab >>Trapping in bottlenecks: Interplay between microscopic dynamics and large scale effects
2017 (English)In: Physica A: Statistical Mechanics and its Applications, ISSN 0378-4371, E-ISSN 1873-2119, Vol. 488, no 11, p. 30-38Article in journal (Refereed) Published
Abstract [en]

We investigate the appearance of trapping states in pedestrian flows through bottlenecks as a result of the interplay between the geometry of the system and the microscopic stochastic dynamics. We model the flow through a bottleneck via a Zero Range Process on a one-dimensional periodic lattice. Particle are removed from the lattice sites with rates proportional to the local occupation numbers. The bottleneck is modeled by a particular site of the lattice whose updating rate saturates to a constant value as soon as the local occupation number exceeds a fixed threshold. We show that for any finite value of the threshold the stationary particle current saturates to the limiting bottleneck rate when the total particle density in the system exceeds a critical value corresponding to the bottleneck rate itself.

Place, publisher, year, edition, pages
Elsevier, 2017
Keywords
Pedestrian flows through bottlenecks, Trapping, Condensation, Stochastic modeling, Interacting particle systems
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-56724 (URN)10.1016/j.physa.2017.07.001 (DOI)
Note

Fulltexten är den inskickade versionen och har inte genomgått peer-review.

Available from: 2017-07-03 Created: 2017-07-03 Last updated: 2017-12-07Bibliographically approved
Artale Harris, P., Cirillo, E. N. . & Muntean, A. (2017). Weak solutions to Allen-Cahn-like equations modelling consolidation of porous media. IMA Journal of Applied Mathematics, 82(1), 224-250
Open this publication in new window or tab >>Weak solutions to Allen-Cahn-like equations modelling consolidation of porous media
2017 (English)In: IMA Journal of Applied Mathematics, ISSN 0272-4960, E-ISSN 1464-3634, Vol. 82, no 1, p. 224-250Article in journal (Refereed) Published
Abstract [en]

We study the weak solvability of a system of coupled Allen–Cahn-like equations resembling cross-diffusion which arises as a model for the consolidation of saturated porous media. Besides using energy-like estimates, we cast the special structure of the system in the framework of the Leray–Schauder fixed-point principle and ensure in this way the local existence of strong solutions to a regularized version of our system. Furthermore, weak convergence techniques ensure the existence of weak solutions to the original consolidation problem. The uniqueness of global-in-time solutions is guaranteed in a particular case. Moreover, we use a finite difference scheme to show the negativity of the vector of solutions.

Place, publisher, year, edition, pages
Oxford University Press, 2017
Keywords
weak solutions; cross-diffusion system; energy method; Leray–Schauder fixed-point theorem; finite differences; consolidation of porous media
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-40730 (URN)10.1093/imamat/hxw013 (DOI)000393103500009 ()
Available from: 2016-02-26 Created: 2016-02-26 Last updated: 2017-07-06Bibliographically approved
Vo Anh, K. & Muntean, A. (2016). A Note on Iterations-based Derivations of High-order Homogenization Correctors for Multiscale Semi-linear Elliptic Equations. Applied Mathematics Letters, 58, 103-109
Open this publication in new window or tab >>A Note on Iterations-based Derivations of High-order Homogenization Correctors for Multiscale Semi-linear Elliptic Equations
2016 (English)In: Applied Mathematics Letters, ISSN 0893-9659, E-ISSN 1873-5452, Vol. 58, p. 103-109Article in journal (Refereed) Published
Abstract [en]

This Note aims at presenting a simple and efficient procedure to derive the structure of high-order corrector estimates for the homogenization limit applied to a semi-linear elliptic equation posed in perforated domains. Our working technique relies on monotone iterations combined with formal two-scale homogenization asymptotics. It can be adapted to handle more complex scenarios including for instance nonlinearities posed at the boundary of perforations and the vectorial case, when the model equations are coupled only through the nonlinear production terms.

Keywords
Homogenization, Justification of the asymptotics, Corrector estimates
National Category
Natural Sciences Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-40584 (URN)10.1016/j.aml.2016.02.009 (DOI)000375523100016 ()
Available from: 2016-02-20 Created: 2016-02-20 Last updated: 2017-11-30Bibliographically approved
Khoa, V. A. & Muntean, A. (2016). Asymptotic analysis of a semi-linear elliptic system in perforated domains: Well-posedness and correctors for the homogenization limit. Journal of Mathematical Analysis and Applications, 439(1), 271-295
Open this publication in new window or tab >>Asymptotic analysis of a semi-linear elliptic system in perforated domains: Well-posedness and correctors for the homogenization limit
2016 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 439, no 1, p. 271-295Article in journal (Refereed) Published
Abstract [en]

In this study, we prove results on the weak solvability and homogenization of a microscopic semi-linear elliptic system posed in perforated media. The model presented here explores the interplay between stationary diffusion and both surface and volume chemical reactions in porous media. Our interest lies in deriving homogenization limits (upscaling) for alike systems and particularly in justifying rigorously the obtained averaged descriptions. Essentially, we prove the well-posedness of the microscopic problem ensuring also the positivity and boundedness of the involved concentrations and then use the structure of the two scale expansions to derive corrector estimates delimitating this way the convergence rate of the asymptotic approximates to the macroscopic limit concentrations. Our techniques include Moser-like iteration techniques, a variational formulation, two scale asymptotic expansions as well as energy-like estimates. 

Keywords
Corrector estimates, Homogenization, Elliptic systems, Perforated domains
National Category
Mathematics
Research subject
Mathematics
Identifiers
urn:nbn:se:kau:diva-41993 (URN)10.1016/j.jmaa.2016.02.068 (DOI)000372941500016 ()
Available from: 2016-05-11 Created: 2016-05-11 Last updated: 2017-11-30Bibliographically approved
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Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0002-1160-0007

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