Exponential attractors and inertial manifolds for a class of generalized nonlinear Kirchhoff-Sine-Gordon equation*

Abstract

In this paper,we consider a class of generalized nonlinear Kirchhoff-Sine-Gordon equation in n dimensional space.We first prove the squeezing property of the nonlinear semigroup associated with this equation and the existence of exponential attractors.Then using the Hadamards graph transformation method,the existence of inertial manifolds of the equation is obtained when N is sufficiently large.