Remarks on an elliptic problem arising in weighted energy estimates for wave equations with space-dependent damping term in an exterior domain

Abstract

This paper is concerned with weighted energy estimates and di usion phenomena for the initial-boundary problem of the wave equation with space-dependent damping term in an exterior domain. In this analysis, an elliptic problem was introduced by Todorova and Yordanov. This attempt was quite useful when the coeffcient of the damping term is radially symmetric. In this paper, by modifying their elliptic problem, we establish weighted energy estimates and di usion phenomena even when the coeffcient of the damping term is not radially symmetric.

Keywords

• Damped wave equation| elliptic problem| exterior domain| weighted energy estimates| diffusion phenomena