Global Well-posedness And Attractor For A Class Of Kirchhoff Wave Mode With Strong Damping

The paper is considered with global well-posedness and attractor for a class of wave mode with strong damping:utt-M(??u?2)?u-?ut+h(ut)+g(u)=f(x).where,M(s)=1+sm/2,m?1,f(x)is external force term.In this paper,when the growth exponent q and p of the nonlinear terms h(u+)and g(u)satisfies 1?q?q*?N+2/(N-2)+,1?p<min {m+1,q*}and p=m+1<q*,the above equation has unique weak and strong solutions in the phase space X=V1 × L2 and the strong solution space X1=V2 × V1 respectively.when t>0,the weak and strong solutions have higher partial regularity,and the existence of global attractors and exponential attractors of solution semigroups in the phase space X and the strong solution space X1 respectively.Moreover,we show the existence of attractors whose compactness,attractiveness and boundedness of the fractional dimension are in the regularized space.