Applications of Mathematics, Vol. 68, No. 2, pp. 153-169, 2023
Multiscale homogenization of nonlinear hyperbolic-parabolic equations
Abdelhakim Dehamnia, Hamid Haddadou
Received August 3, 2021. Published online June 17, 2022.
Abstract: The main purpose of the present paper is to study the asymptotic behavior (when $\varepsilon\to0$) of the solution related to a nonlinear hyperbolic-parabolic problem given in a periodically heterogeneous domain with multiple spatial scales and one temporal scale. Under certain assumptions on the problem's coefficients and based on a priori estimates and compactness results, we establish homogenization results by using the multiscale convergence method.
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Affiliations: Abdelhakim Dehamnia (corresponding author), Laboratory of Physics Mathematics and Applications, École Normale Supérieure, 16308 Vieux-Kouba, Algiers, Algeria, e-mail: abdelhakimdehamnia@gmail.com; Hamid Haddadou, LCSI Laboratory, École Nationale Supérieure d'Informatique (ESI ex INI), Oued Smar, Algiers, Algeria, e-mail: h_haddadou@esi.dz
