Time-dependent global attractors for strongly damped wave equation with critical exponent

Abstract:

In this paper, we are concerned with the longtime behavior of the non-autonomous strongly damped wave equations. We first obtain the dissipativity of the process associated with the equations. Then, by using the skill of the operator decomposition, we prove the asymptotic compactness of the process. Finally, we give out the existence of the time-dependent attractors for the equation.