Dynamics For A Strongly Damped Wave Equation

In this thesis, we consider the long-time behavior for the following strong-ly damped wave equation denned on a bounded domain Ω∈R3with smooth boundary (?)Q:For the case g∈L2(Ω). the dynamics of solutions to the above equation has been the object of extensive studies. Here, we mainly consider the case g∈H-1.The main achievements and novelty in this thesis are two parts:the first one is that we prove some asymptotic regularity (possible optimal) for the solution without the quasi-monotone condition f’(s)≥-k; the second one is that we prove the existence of a finite-dimensional exponential attractor under the same natural assumptions. To overcome the difficulty brought by the lower regularity of forcing term, some new and refined decompositions of the solution have been devised and presented.