The Initial Boundary Value Problem For A Class Of Nonlinear Wave Equation

In this paper, we study the global existence, the asymptotic behavior of weak solution and the blowup of solutions to the initial boundary value problem for a class of nonlinear wave equations with nonlinear dissipative term:where Ω (?) R~N is a bounded domain with smooth boundary (?)Ω, A is the Laplace operator, v indicates the outer unit normal at (?)Ω, σ_i(s)(i = 1, ??? , N),f(s) are given nonlinear functions. We prove the problem (1)-(3) admits a unique global weak solution under the small initial data and disuss asymptotic behavior of the solution, Moreover, the sufficient conditions of blow up of the solutions in finite time are given.In Chapter 2, by a Galerkin approximation scheme, as well as combining it with the potential well method, we prove the global existence and uniqueness of weak solution for the problem (1)-(3). by V. Komornik inequality, We prove the asymptotic behavior of the weak solution . In Chapter 3, by an energy method, we study the blow up of the solutions for problem (1)-(3) in finite time. The main results are as follows:Theorem 1 Assume thatand where...