本文研究一类含奇异项的半线性抛物方程的初边值问题,给出了该问题的古典解整体存在或发生猝灭现象的判据以及猝灭解的生命跨度估计。同时,还用上述结果研究了一类含超Sobolev临界指标的半线性椭圆方程的Dirichlet边值问题,获得了正解的存在性结果。

Initial-boundary value problem for a class of semilinear parabolic equation with singular term is studied in this paper. Criterions for the existence of global classical solution or for the appearance of quenching phenomenon of the above problem are given. Also, life span of the quenching solution is estimated. As the same time, the above results are used to study Dirichlet problem for a class of semiliear elliptic equation with supercritical Sobolev exponent and an existence result of positive solutions is obtained.