一类拟线性发展方程解的Blow-up

Blow-up of Solution of a Class of Quasilinear Evolution Equation

用特征函数法研究相当广泛的一类拟线性发展方程 (包括非线性拟双曲方程与强阻尼非线性波动方程 )的初边值问题解的非整体存在性与blow_up ,证明了在某些条件下 ,解必在有限时间内blow_up .

By using eigenfunction method we studied the global nonexistence and blow_up of solution of the initial_boundary value problem for a class of quasilinear evolution equation (including nonlinear psedohyperbolic equation and strongly damped nonlinear wave equation),and proved that under some conditions the solution must blow_up in a finite time.