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Stability of the blow-up time and the blow-up set under perturbations

Arrieta Algarra, José María and Ferreira de Pablo, Raúl and Pablo, Arturo de and Rossi, Julio D. (2010) Stability of the blow-up time and the blow-up set under perturbations. Discrete and Continuous Dynamical Systems. Series A., 26 (1). pp. 43-61. ISSN 1553-5231

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Abstract

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 some 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 special 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


Item Type:Article
Uncontrolled Keywords:Stability; Blow-up; Perturbations; Perturbations of the domain; Perturbations of parameters; Blow-up rates; Perturbations on the initial condition
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:13936
Deposited On:23 Nov 2011 15:21
Last Modified:06 Feb 2014 09:56

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