Record number :

1561828

Title of article :

Homogenization and corrector for the wave equation with discontinuous coefficients in time

Author/Authors :

Carmen and Casado-Dيaz، نويسنده , , Juan and Couce-Calvo، نويسنده , , Julio and Maestre، نويسنده , , Faustino and Martيn-Gَmez، نويسنده , , José D.، نويسنده ,

Issue Information :

دوهفته نامه با شماره پیاپی سال 2011

Pages :

18

From page :

664

To page :

681

Abstract :

In this paper we analyze the homogenization of the wave equation with bounded variation coefficients in time, generalizing the classical result, which assumes Lipschitz-continuity. We start showing a general existence and uniqueness result for a general sort of hyperbolic equations. Then, we obtain our homogenization result comparing the solution of a sequence of wave equations to the solution of a sequence of elliptic ones. We conclude the paper making an analysis of the corrector. Firstly, we obtain a corrector result assuming that the derivative of the coefficients in the time variable is equicontinuous. This result was known for non-time dependent coefficients. After, we show, with a counterexample, that the regularity hypothesis for the corrector theorem is optimal in the sense that it does not hold if the time derivative of the coefficients is just bounded.

Keywords :

homogenization , Corrector , wave equation

Journal title :

Journal of Mathematical Analysis and Applications

Serial Year :

2011

Link To Document :