非线性卷积拟双曲型积分微分方程解的Blow up

Blow up of solutions for nonlinear convolutional integrodifferential equations of pseudohyperbolic type

考虑了两类非线性卷积拟双曲型积分微分方程初边值问题解的blowup.借助于特征函数法和Jensen不等式,证明了在非线性函数φ、f和初始数据的某些条件下,所论问题的局部解在有限时间内blowup.

Blow up of solutions of initial boundary value problems for two classes of nonlinear convolution integrodifferential equations of pseudohyperbolic type is considered in this paper.By the aid of the eigenfunction method and Jensen inequality, local solutions of the problems blow up in finite time under certain conditions of the nonlinear functions φ,f and the initial data is proved.