具强阻尼黏弹性波动方程组解的指数衰退

Exponential Decay of Solutions of a Viscoelastic Wave Equation with Strong Damping

研究一类包含强阻尼项的非线性波动方程组的初边值问题.根据方程组的特点,构造了能量函数,研究能量函数的性质,并利用所得结果、积分估计及Poincaré不等式,得到了在一定条件下该问题解的指数衰退性质.

The aim of this paper is to investigated the initial boundary value problem for a system of nonlinear wave equations involving strong damping terms. The authors constructed an energy functional and studied the properties of the functional in view of the character of the system. With the above results,integral estimates and Poincaré＇s inequality,an exponentially decay result of the solutions to the problem was obtained under suitable assumptions.