Exponential attractors for the strongly damped wave equation

摘要

In this paper, we study the longtime dynamics to a strongly damped wave equation. First, in the critical case, we prove by the l-trajectories method that the related solution semigroup has the exponential attractor. Second, in the subcritical case, we give an explicit upper bound of the fractal dimension of the exponential attractor in terms of the data of the equation.