| 关于猝灭问题的一些结果及其应用 |
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| 引用本文： | 戴求亿,顾永耕.关于猝灭问题的一些结果及其应用[J].数学学报,2003,46(5):985-992. |
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| 作者姓名： | 戴求亿 顾永耕 |
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| 作者单位： | 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 |
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| 基金项目： | 国家自然科学基金(10171029) |
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| 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。
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| 关 键 词： | 半线性抛物方程 猝灭现象 整体解 |
| 文章编号： | 0583-1431(2003)05-0985-08 |
| 修稿时间： | 2001年12月13 |
Some Results on Quenching Problem and Its Applications |
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| Qiu Yi DAI.Some Results on Quenching Problem and Its Applications[J].Acta Mathematica Sinica,2003,46(5):985-992. |
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| Authors: | Qiu Yi DAI |
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| Affiliation: | Qiu Yi DAI (Department of Applied Mathematics, Hunan University, Changsha 410082, P. R. China)
Yong Geng GU (Department of Mathematics, Hunan Normal University, Changsha 410081, P. R. China) |
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| Abstract: | 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. |
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| Keywords: | Semilinear parabalic equation Quenching phenomenon Global solution |
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