非线性黏弹性波动方程解的爆破

Blow up of Solution for Nonlinear Viscoelastic Wave Equation

研究了带有非线性阻尼和源项的黏弹性波动方程解的存在性及爆破性问题。特别地,该方程主部系数μ(t)是关于时间t的一个函数。在假设条件下,获得了该问题局部解的存在性。在局部解存在前提下,利用势井理论和能量方法证明了当初始能量有上界时,解在有限时间内爆破,并给出了关于解的爆破时间估计。

The existence and blow-up of the solution for a viscoelastic wave equation with nonlinear damping and source terms were considered. Especially,the coefficient of the principal part of the equation μ( t) was time t dependent function. Under some assumptions,the existence of local solution was proved. When the initial energy has an upper bound and the local solution exist,the solution blows up in finite time by using the potential well theory and energy method. In addition,an estimate about the blow-up time of the solution was obtained.