A Class Of Strongly Damped Quasi-linear Wave Equation

In this paper,we consider the existence of finite-dimensional global and exponential attractors for the strongly damped quasi-linear wave equation:We firstly prove the existence of global solution in H01(Ω)×L2(Ω)by the usual contraction mapping principle,and.introduced the function of blocking to start an estimate of 2nd order;furtherly the problem admits a unique solution u∈C((0,+∞);H2(Ω)∩H01(Ω))∩C1((0,+∞);L2(Ω)).Finally,we apply the method of L-trajectories to get the existence of weak global and exponential attractors for solution semigroup which have finite fractal and Hausdorff dimension(see [3] [5]).At last,some examples are given.