Energy Decay For Two Kinds Of Nonlinear Viscoelastic Partial Differential Equations With Damping Term

In this paper,we mainly study two kinds of nonlinear viscoelastic partial differential equations with damping term.In the partial differential equation,it is very important that the research will promote the further development of the theory of partial differential equations.Nonlinear viscoelastic wave equation with damping term is an important part of nonlinear partial differential equation.(1)A nonlinear viscoelastic wave equation with strong damping is presented as follows.where ? is a bounded domain of Rn,(n?1)with a smooth boundary(?)? and p>m>2,g:R+?R+ is a positive nonincreasing function,and(2)A nonlinear viscoelastic wave equation with nonlinear damping is presented as follows.where H01(?)is a bounded domain of ? with a smooth boundarv(?)?,p>m>2,g:R+?R+ is a positive nonincreasing function,andThe first chapter introduces the background and its recent development,and analyzes the motivations of this thesis,and gives some basic notions and related notations.The second chapter mainly uses the relevant concepts and properties defined in the above chapter,we can get some similar equalities on Decay estimates for the nonlinear viscoelastic wave equation with a damping term.The third chapter mainly uses the relevant concepts and properties defined in the above two chapters,we can get some similar equalities on Decay estimates for the nonlinear viscoelastic wave equation with a nonlinear damping term.