带有耗散梯度函数的抛物方程爆破与有效性分析

Blow-up and Effectiveness Analysis in a Parabolic Equation with Dissipative Gradient Function

通过建立合适的Sobolev型不等式,解决一类混合边界条件下含有耗散梯度函数的抛物方程解的爆破问题,当问题解发生爆破时,使用两种方法得到了其爆破时间的下界估计,并给出这些方法的有效性分析.

By establishing an appropriate Sobolev inequality,we solved the blow-up problem of solutions of a class of parabolic equation with dissipative gr adient functions under mixed boundary conditions.Furthermore,two methods were us ed to obtain estimates of the lower bound of blow-up time for blow-up solutions,and the effectiveness of the these methods was analyzed.