Global Existence Uniqueness And Uniform Energy Decay Of Nonlinear Viscoelastic Kirchhoff-type Equation With Acoustic Boundary Conditions

This paper is concerned with the existence, the uniqueness and the uniform decay for the solution of the following viscoelastic Kirchhoff-type equation with acoustic boundary conditions,This dissertation is divided into five sections.In the first section, we introduce the importance and the international re-search progress of the nonlinear viscoelastic Kirchhoff-type equation, we also state the hypotheses for the problem.In the second section, we list some preliminaries such as the Sobolev imbed-ding theorem, several kinds of important inequalities and so on.In the third section, we prove the existence and the uniqueness of the solution to the problem (1.1)-(1.4). The proof of the existence includes Faedo-Galerkin approximation, some prior estimates, limiting process.In the forth section, under suitable conditions, we prove the uniform decay of the solution: In the fifth section, under suitable conditions, we prove the uniform decay of the solution: by implying the functional where ε,μ are arbitrary positive constants, and the definitions of F(t),Φ(t) are given by...