Record number :
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 :
From page :
To page :
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 :
Link To Document :