一类四阶非线性波动方程柯西问题解的爆破

Blow-up of the Solution to the Cauchy Problem for a Class of Fourth-order Nonlinear Wave Equations

研究非线性阻尼项与源项的竞争对具有强阻尼项的四阶波动方程解的影响.得到源项强于阻尼项时(即当m<p),初始能量为正,且初始数据满足一定条件时,解将在有限时间内爆破,并得到解生命跨度的上界估计.

In this paper,the fourth order wave equation with nonlinear damping and source term is considered.We show that the solution blows up in finite time if m<p,the initial energy is positive and the initial value satisfies a suitable condition.