Improved conditions for single-point blow-up in reaction-diffusion systems

被引：14
作者：
Mahrnoudi, Nejib [1 ]
Souplet, Philippe [2 ]
Tayachi, Slim [1 ]
机构：
[1] Univ Tunis El Manan, Fac Sci Tunis, Dept Math, Lab Equat Derivees Partielles LR03ES04, Tunis 2092, Tunisia
[2] Univ Paris 13, CNRS UMR 7539, Sorbonne Paris Cite, Lab Anal Geometrie & Applicat, F-93430 Villetaneuse, France
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2015年 / 259卷 / 05期
关键词：
Nonlinear initial boundary value problems; Nonlinear parabolic equations; Reaction diffusion systems; Asymptotic behavior of solutions; Single-point blow-up; Blow-up profile; II BLOWUP; BEHAVIOR;
D O I：
10.1016/j.jde.2015.03.024
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study positive blowing-up solutions of the system: u(t)-delta Delta u = v(P), v(t)-Delta v = u(q) , as well as of some more general systems. For any p, q> 1, we prove single-point blow-up for any radially decreasing, positive and classical solution in a ball. This improves on previously known results in 3 directions: (i) no type I blow-up assumption is made (and it is known that this property may fail); (ii) no equidiffusivity is assumed, i.e. any delta > 0 is allowed; (iii) a large class of nonlinearities F(u, v), G(u, v) can be handled, which need not follow a precise power behavior. As a side result, we also obtain lower pointwise estimates for the final blow-up profiles. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：1898 / 1932
页数：35
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