STABILITY OF THE BLOW-UP TIME AND THE BLOW-UP SET UNDER PERTURBATIONS

被引：1

作者：

Arrieta, Jose M. ^{[1
]}

Ferreira, Raul ^{[1
]}

de Pablo, Arturo ^{[2
]}

Rossi, Julio D. ^{[3
]}

机构：

[1] Univ Complutense Madrid, Dept Matemat Aplicada, E-28040 Madrid, Spain

[2] Univ Carlos III Madrid, Dept Matemat Aplicada, Leganes 28911, Spain

[3] Campus Cantoblanco UAM, IMDEA Matemat, Madrid, Spain

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2010年 / 26卷 / 01期

关键词：

Stability; blow-up; perturbations; DIFFUSION EQUATIONS; HEAT-EQUATIONS; DEPENDENCE; CONVERGENCE; RESPECT;

D O I：

10.3934/dcds.2009.26.43

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we prove a general result concerning continuity of the blow-up time and the blow-up set for an evolution problem under perturbations. This result is based on sonic convergence of the perturbations for times smaller than the blow-up time of the unperturbed problem together with uniform bounds on the blow-up rates of the perturbed problems. We also present several examples. Among them we consider changing the spacial domain in which the heat equation with a power source, takes place. We consider rather general perturbations of the domain and show the continuity of the blow-up time. Moreover, we deal with perturbations on the initial condition and on parameters in the equation. Finally, we also present some continuity results for the blow-up set.

引用

页码：43 / 61

页数：19

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