Multiscale homogenization of nonlinear hyperbolic-parabolic equations

Abstract

The main purpose of the present paper is to study the asymptotic behavior (when ε → 0) 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.