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  • 1.
    Fatima, Tasnim
    et al.
    Eindhoven Univ Technol, Ctr Anal Sci Comp & Applicat, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands.
    Muntean, Adrian
    Eindhoven University of Technology.
    Ptashnyk, Maria
    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)
  • 2. Lin, G.
    et al.
    Zhang, Y.
    Cheng, X.
    Gulliksson, M.
    Forssen, P.
    Fornstedt, T.
    A regularizing Kohn-Vogelius formulation for the model-free adsorption isotherm estimation problem in chromatography2018In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 97, no 1, p. 13-40Article in journal (Refereed)
    Abstract [en]

    Competitive adsorption isotherms must be estimated in order to simulate and optimize modern continuous modes of chromatography in situations where experimental trial-and-error approaches are too complex and expensive. The inverse method is a numeric approach for the fast estimation of adsorption isotherms directly from overloaded elution profiles. However, this identification process is usually ill-posed. Moreover, traditional model-based inverse methods are restricted by the need to choose an appropriate adsorption isotherm model prior to estimate, which might be very hard for complicated adsorption behavior. In this study, we develop a Kohn-Vogelius formulation for the model-free adsorption isotherm estimation problem. The solvability and convergence for the proposed inverse method are studied. In particular, using a problem-adapted adjoint, we obtain a convergence rate under substantially weaker and more realistic conditions than are required by the general theory. Based on the adjoint technique, a numerical algorithm for solving the proposed optimization problem is developed. Numerical tests for both synthetic and real-world problems are given to show the efficiency of the proposed regularization method.

  • 3.
    Lind, Martin
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Muntean, Adrian
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Richardson, Omar
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
    Well-posedness and inverse Robin estimate for a multiscale elliptic/parabolic system2018In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 97, no 1, p. 89-106Article in journal (Refereed)
    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.

  • 4.
    Muntean, Adrian
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Preface2018In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 97, no 1, p. 1-2Article in journal (Refereed)
  • 5.
    Muntean, Adrian
    et al.
    Eindhoven Institute of Technology, Netherlands.
    Ptashnyk, M.
    Univ Dundee, Div Math, Dundee DD1 4HN, Scotland.
    Showalter, R. E.
    Oregon State Univ, Dept Math, Corvallis, OR 97331 USA.
    Analysis and Approximation of Microstructure Models2012In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 91, no 6, p. 1053-1054Article in journal (Refereed)
  • 6.
    Shestopalov, Yuri
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Smirnov, Yury
    Penza State Univ, Dept Math & Supercomp, Penza 440017, Russia..
    Eigenwaves in waveguides with dielectric inclusions: completeness2014In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 93, no 9, p. 1824-1845Article in journal (Refereed)
    Abstract [en]

    We formulate the definition of eigenwaves and associated waves in a nonhomogeneously filled waveguide using the system of eigenvectors and associated vectors of a pencil and prove its double completeness with a finite defect or without a defect. Then, we prove the completeness of the system of transversal components of eigenwaves and associated waves as well as the mnimality' of this system and show that this system is generally not a Schauder basis. This work is a continuation of the paper Eigenwaves in waveguides with dielectric inclusions: spectrum. Appl. Anal. 2013. doi:10.1080/00036811.2013.778980 by Y. Smirnov and Y. Shestopalov. Therefore, we omit the problem statements and all necessary basic definitions given in the previous paper.

  • 7.
    Shestopalov, Yuri
    et al.
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
    Smirnov, Yury
    Penza State Univ, Dept Math & Supercomp, Penza 440017, Russia..
    Eigenwaves in waveguides with dielectric inclusions: spectrum2014In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 93, no 2, p. 408-427Article in journal (Refereed)
    Abstract [en]

    We consider fundamental issues of the mathematical theory of the wave propagation in waveguides with inclusions. Analysis is performed in terms of a boundary eigenvalue problem for the Maxwell equations which is reduced to an eigenvalue problem for an operator pencil. We formulate the definition of eigenwaves and associated waves using the system of eigenvectors and associated vectors of the pencil and prove that the spectrum of normal waves forms a non-empty set of isolated points localized in a strip with at most finitely many real points.

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