DYNAMICS FOR THE DAMPED WAVE EQUATIONS ON TIME-DEPENDENT DOMAINS

摘要

We consider the asymptotic dynamics of a damped wave equations on a time-dependent domains with homogeneous Dirichlet boundary condition, the nonlinearity is allowed to have a cubic growth rate which is referred to as the critical exponent. To this end, we establish the existence and uniqueness of strong and weak solutions satisfying energy inequality under the assumption that the spatial domains O-t in R-3 are obtained from a bounded base domain O by a C-3-diffeomorphism r (., t). Furthermore, we establish the pullback attractor under a slightly weaker assumption that the measure of the spatial domains are uniformly bounded above.