Attractors For Wave Equations With Nonlinear Interior And Surface Damping

This paper is concerned with a wave equation with an acoustic boundary condition, whose interior and surface damping are nonlinear. We prove the existence of the attractor for the wave equation. And we estimate the Hausdorff dimension of the attractor for the wave equation with linear interior and surface damping. This paper is divided into three parts:In the first chapter, we introduced the problem and the physical background, domestic and foreign research and some basic knowledge.In the second chapter, the nonlinear damped wave equations with an acoustic boundary condition yield a semigroup. By using S. Zhou and X. Fan’s method[11-12], we estimate a type of operator which is useful to obtain the existence of absorbing sets and asymptotical compactness for the semigroup.When the interior damping and surface damping are linear, in the last chapter, we estimate the Hausdorff dimension for the attractor. Since the Hausdorff dimension of exponential attractor must be finite, our dimension result is a useful supplement for S.Frigeri’s results[1] on exponential attractor.