On thermal explosion in porous media

被引：5

作者：

Gordon, Peter ^{[1
]}

机构：

[1] New Jersey Inst Technol, Dept Math Sci, Newark, NJ 07102 USA

来源：

NONLINEARITY | 2010年 / 23卷 / 06期

关键词：

COMPLETE BLOW-UP; EIGENVALUE PROBLEMS; POSITIVE SOLUTIONS;

D O I：

10.1088/0951-7715/23/6/009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a model of thermal explosion in porous media which is a natural generalization of the well-known problem of self-ignition introduced by (Gelfand 1963 Am. Math. Soc. Trans. 29 295-381). We rigorously prove that, similar to the Gelfand-Barenblatt problem, the thermal explosion (finite time blow-up of all solutions for the problem with non-negative initial data) occurs exclusively due to the absence of a weak solution of the corresponding stationary problem.

引用

页码：1433 / 1447

页数：15

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