Decay Of Energy For Some Hyperbolic Partial Differential Equations

In this paper,we study decay rate of solutions of some hyperbolic partial differential equations.Firstly,we concern decay of energy for a quasilinear wave equation with viscosity,we use a so-called energy perturbation method to establish decay rate of solutions in terms of energy norm for a class of nonlinear functions.With the help of a comparison lemma of differential inequalities we establish a relationship between decay rate of solutions and f;Secondly,we study the large-time behavior of energy for a N-dimensional dissipative anisotropic elastic system,we use Nakao’s inequality and Zuazua’s theory of estimates to establish polynomial decay of energy.