强阻尼非线性波动方程解的渐近性质

Asymptotic behavior of solution for strongly damped nonlinear wave equations

研究一类带有Dirichlet边界条件的强阻尼非线性波动方程的初边值问题。关于该方程整体强解的存在性研究已经得到了很好的结果,因此仅对解的渐近性质进行讨论。对该问题进行简化,并对非线性项给予适当的约束条件,利用乘子法和积分估计的方法研究该问题解的渐近性质,并得到较好的结果,即解以指数形式趋于零。

The initial-boundary value problem of strongly damped nonlinear wave equations with Dirichlet boundary conditions is studied.Since the global existence of strong solution has been well studied,here just the asymptotic behaviors of solutions are considered.First the problem is simplified,and some assumption on the nonlinear source term are added.By using the multiplier method and integral estimates method,the asymptotic behaviors of global solution under some conditions on nonlinear terms are proved.It shows that the solutions can convergence to zero in an exponential form.