Homogenization of nonlinear parabolic equations with hysteresis
Achille Landri Pokam Kakeu, Jean Louis Woukeng · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 2020
Abstract 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.