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 16:21 |
| Last Modified: | 23 Nov 2011 16:21 |
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