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On degenerate coupled transport processes in porous media with memory phenomena
Author(s) -
Beneš Michal,
Pažanin Igor
Publication year - 2018
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201700158
Subject(s) - degenerate energy levels , bounded function , porous medium , nonlinear system , mathematical analysis , mathematics , neumann boundary condition , boundary value problem , weak solution , porosity , materials science , physics , quantum mechanics , composite material
In this paper we prove the global existence of weak solutions to degenerate parabolic systems coupled with an integral condition arising from the fully coupled moisture movement, transport of dissolved chemical species and heat transfer through porous materials. The problem under consideration covers a large range of problems including hygro‐thermo‐chemical modelling of concrete at early ages taking into account hydration (memory) phenomena. In the model, all changes of material properties are expressed as functions of state variables and the memory function (the so called hydration degree). Physically relevant mixed Dirichlet‐Neumann boundary conditions and initial conditions are considered. Existence of global weak solutions of the problem is proved by means of semidiscretization in time, proving necessary uniform estimates and by passing to the limit from discrete approximations. Degeneration occurs in the nonlinear transport coefficients which are not assumed to be bounded below and above by positive constants. Degeneracies in transport coefficients are overcome by proving suitable a‐priori L ∞ ‐estimates based on De Giorgi and Moser iteration technique.