A note on damped wave equations with a nonlinear dissipation in non-cylindrical domains

Abstract

In this paper, we study the large time behavior of a class of wave equation with a nonlinear dissipation in non-cylindrical domains. The result we obtained here relaxes the conditions for the nonlinear term coefficients (in precise, that is $\beta(t)|u|^\rho u$) in \cite{alb} and \cite{ha} (which require $\beta(t)$ to be a constant or $\beta(t)$ to be decreasing with time $t$) and has less restriction for the defined regions.