Long-time Behavior Of A Class Of Nonlinear Strongly-damped Wave Equation

This paper studies the following quasi-linear strong-damped wave equation in a smooth bounded domainΩRNwhere△is a Laplacian with respect to the variable x∈Ω.f are given external forces, and external forceΦ,g will be specified later. The existence of solutions are established by Galerkin emthod; the uniqueness of solutions in the case where the growth exponent of the non-linearityΦ,g is less than(N+2)/(N-2)+,(N+4)/(N-4)+ are easy to get；by using the method of L-trajectories,the existence of a weak global at-tractor and weak exponential attractors for the corresponding dynamical system are also established.Moreover,we can also prove the uniqueness of solutions in the case where the growth exponents of the non-linearityΦ,g are no more than(N+2)/(N-2)+,(N+4)/(N-4)+...