Finite Dimensional Behavior for Forced Nonlinear Sobolev-Galpern Equations

Abstract

This paper deals with the asymptotic behavior of solutions for the nonlinear Sobolev-Galpern equations. We first show the existence of the global weak attractor in $$ H^{2} {\left( \Omega \right)} \cap H^{1}_{0} {\left( \Omega \right)} $$ for the equations. And then by an energy equation we prove that the global weak attractor is actually the global strong attractor. The finite-dimensionality of the global attractor is also established.