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Homogenization of nonlinear parabolic equations with hysteresis
Author(s) -
Pokam Kakeu Achille Landri,
Woukeng Jean Louis
Publication year - 2020
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.201900323
Subject(s) - homogenization (climate) , mathematics , nonlinear system , monotone polygon , mathematical analysis , boundary value problem , parabolic partial differential equation , monotonic function , operator (biology) , hysteresis , partial differential equation , physics , geometry , biodiversity , ecology , repressor , quantum mechanics , gene , transcription factor , biology , biochemistry , chemistry
This work is concerned with the homogenization of initial boundary value parabolic equations with hysteresis, containing nonlinear monotone operators in the diffusion term. We make use of the sigma‐convergence concept together with the properties of hysteresis operator to derive the homogenized problem. The homogenized operator is obtained in terms of a solution of a nonlinear corrector problem posed and solved in the usual sense of distributions. We also provide an approximation scheme for the homogenized coefficient.