Behavior Of A Class Of Generalized Nonlinear Wave Equation

The Viscoelastic equation with memory source is a important nonlinear partial differential equation, which is a mathematics model for solidity mechanics. This paper mainly studied the long-time behavior for a nonlinear viscoelastic wave equation with damping and source terms.Firstly, the paper obtained a equivalent equation by a variable substitution. When the source term was in the right side, and we proved a blow up result for the solution with proper conditions. Secondly, when the source term was in the left side and added a force term to the right side, we obtained the existence and uniqueness of solutions by Galerkin method, and the existence of the global attractor with proper conditions by Semi-group Theory.