Asymptotic Behavior Of The Berger Type Equation

In this paper,we consider the initial boundary vaule problem of the non-degenerate Berger Type wave equation with nonlinear damping: where M(r)= 1+r(?),m≥1.Ω(?) RN is a bounded domain with smooth boundary (?)Ω.In this paper,by virtue of operator theory,first we get the Cauchy problem which equivalents the original one as follows where A=Δ2. Then,we prove the existence and uniqueness of strong solution. At the basis of this,we prove the existence and uniqueness of weak solution, so,we can use theory of asymptotically compact to prove that the above mentioned dynamical system possesses a global attractor (?). At last we can also prove (?) has finite fracal dimension by the method of a-contration.