Long-time Dynamics For A Class Of Nonlinear Wave Equations With Structural Damping

In this paper, we are concerned with the existence of global attractor and exponential attractor for the quasi-linear structural damped wave equation where is a bounded domain with smooth boundary ????, the nonlinear term is f?u? and g is external force. we suppose that the growth exponent of f is q : 1? g < ?, we prove that the solution for the equation is of higher global regularity as In natural energy space? =?W2,p+1?H01?×L2 the existence of finite-dimensional global and exponential attractors is established as . When p'?p < p? , we establish the existence of??,?-?? global attractor ?weak global attractor? and ??,?-?? exponential attractor ?weak exponential attractor?, where ?_-?=W^2-?,p+1×L²,?_-?=V_?×V_-?.