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.