Global Attractors For Nonlinear Wave Equations With Nonlinear Dissipative Terms

The paper is divided into three chapters. In this paper, we show the existence of weak solutions to nonlinear wave equations with nonlinear dissipative terms, and we show the existence, size and some absorbing properties of its global attractors. the main contents are as follows:In the first chapter, we main introduce some useful basic concepts and basic theories which will be used in the paper.In the second chapter, we study the existence of weak solutions to nonlinear wave equations with nonlinear dissipative like |ht(x,t)|qht(x,t). the result is as follows:The equation it has a unique weak solution to h(x,t) ∈ L2(0,T;H01(Ω)),h’(x,t) ∈ L2(0,T;L2(Ω)), h(0)= h0,h’(0)= h1. where A= A(x)= (aij(x)),aij(x)=aji(x) ∈ G1(Ω), ij= 1.2...n. 1/C|ξ|≤aij(x)ξiξj≤C|ξ|2,ξ=(ξ1...ξ2)T ∈Rn.In the third chapter, we study the existence,size and some absorbing properties of global attractors to nonlinear wave equations with nonlinear dissipative like |ht(x, t)|qht(x, t). The result is as follows:Under hypothesis 1-3, the equation there is a global attractor X in the space H01(Ω)×L2(Ω).Furthermore X is included a ball B(R) which is on the space H01(Ω)×L2(Ω).The ball B(R) is centered at O with the radius R=C(M02+L+L).For any bounded set H01(Ω)×L2(Ω),we have the absorbing property dist(U(t)B0,B(R))≤C(B0)(1+t)-1/2λ,...