关于猝灭问题的一些结果及其应用  

Some Results on Quenching Problem and Its Applications

作　　者：戴求亿[1] 顾永耕[2] 

机构地区：[1]湖南大学应用数学系,长沙410082 [2]湖南师范大学数学系,长沙410081

出　　处：《数学学报（中文版）》2003年第5期985-992,共8页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(10171029)

摘　　要：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.

关 键 词：半线性抛物方程 猝灭现象 整体解 

分 类 号：O175.26[理学—数学] O175.25[理学—基础数学]