一类具非线性强耗散项发展方程解的爆破

Blow up of solutions for a class of evolution equations with nonlinear strong dissipation term

研究具非线性强耗散项的发展方程 utt-γuxx=β(uxt) x的初边值问题解的整体非存在性和 blow up.借助于特征函数法和 Jensen不等式 ,证明了在非线性函数和初始数据的某些条件下 ,问题的解在有限时间内 blow up.

The global nonexistence and blow up of solutions of initial boundary value problems for a class of evolution equations with nonlinear strong dissipation term are studied in this paper.With the aid of eigenfunction method and the Jensens inequality,the solutions of these problems blow up in finite time are proved under certain conditions.