Continuity of the blow-up profile with respect to initial data and to the blow-up point for a semilinear heat equation

被引：5

作者：

Khenissy, S. ^{[2
,3
]}

Rebai, Y. ^{[3
,4
]}

Zaag, H. ^{[1
]}

机构：

[1] Univ Paris 13, Inst Galilee, UMR 7539, LAGA, F-93430 Villetaneuse, France

[2] Univ Tunis El Manar, Inst Super Informat, Dept Math Appl, Ariana 2037, Tunisia

[3] Univ Tunis El Manar FST, UR Anal Non Lineaire & Geometrie 03 UR 15 01, Tunis, Tunisia

[4] Univ 7 Novembre Carthage, Fac Sci Bizerte, Dept Math, Jarzouna 7021, Bizerte, Tunisia

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2011年 / 28卷 / 01期

关键词：

BEHAVIOR; NONEXISTENCE; REGULARITY; SET; UNIVERSALITY; EXISTENCE; THEOREMS;

D O I：

10.1016/j.anihpc.2010.09.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider blow-up solutions for semilinear heat equations with Sobolev subcritical power nonlinearity. Given a blow-up point a, we have from earlier literature, the asymptotic behavior in similarity variables. Our aim is to discuss the stability of that behavior, with respect to perturbations in the blow-up point and in initial data. Introducing the notion of "profile order", we show that it is upper semicontinuous, and continuous only at points where it is a local minimum. (c) 2010 Elsevier Masson SAS. All rights reserved.

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页码：1 / 26

页数：26

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