A Family of Inertial Manifolds for a Class of Generalized Kirchhoff-Beam Equations

Abstract

In this paper, we deal with a class of generalized Kirchhoff-Beam equations. At first, we take advantage of Hadamard’s graph to get the equivalent form of the original equations. Then, the inertial manifolds are proved by using spectral gap condition. We gain main result is that the family of inertial manifolds are established under the proper assumptions of nonlinear terms M(s) and N(s).