Determining functionals for damped nonlinear wave equations

Abstract

The paper is devoted to the study of asymptotic behavior as t -> +infinity of solutions of initial boundary value problem for strongly damped nonlinear wave equation and strongly damped Kirchhoff type equation under homogeneous Dirichlet's boundary conditions. We proved that the asymptotic behavior as t -> infinity of solutions of these problem is completely determined by dynamics of finitely many functionals.