Blow-up with logarithmic nonlinearities

被引：5
作者：
Ferreira, Raul
de Pablo, Arturo [1 ]
Rossi, Julio D.
机构：
[1] Univ Carlos III Madrid, Dept Matemat, E-28911 Madrid, Spain
[2] Univ Complutense Madrid, Dept Matemat Aplicada, E-28040 Madrid, Spain
[3] Univ Buenos Aires, Dept Matemat, FCEyN, RA-1428 Buenos Aires, DF, Argentina
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2007年 / 240卷 / 01期
关键词：
blow-up; asymptotic behaviour; nonlinear boundary conditions;
D O I：
10.1016/j.jde.2007.05.004
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the asymptotic behaviour of nonnegative solutions of the nonlinear diffusion equation in the half-line with a nonlinear boundary condition, [GRAPHICS] with p, q,lambda > 0. We describe in terms of p, q and lambda when the solution is global in time and when it blows up in finite time. For blow-up solutions we find the blow-up rate and the blow-up set and we describe the asymptotic behaviour close to the blow-up time, showing that a phenomenon of asymptotic simplification takes place. We finally study the appearance of extinction in finite time. (c) 2007 Elsevier Inc. All rights reserved.
引用
收藏
页码：196 / 215
页数：20
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