Stability of the blow-up time and the blow-up set underperturbations
Copyright policy )Stability of the blow-up time and the blow-up set underperturbations
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
blow-up rates, Perturbations of the domain, Perturbations in context of PDEs, perturbations of parameters, Blow-up, Perturbations of parameters, perturbations on the initial condition, stability, Perturbations, 517.98, Blow-up in context of PDEs, perturbations, https://purl.org/becyt/ford/1.1, https://purl.org/becyt/ford/1, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, Stability in context of PDEs, Semilinear parabolic equations, Stability, blow-up, perturbations of the domain, Blow-up rates, Perturbations on the initial condition, Análisis funcional y teoría de operadores
blow-up rates, Perturbations of the domain, Perturbations in context of PDEs, perturbations of parameters, Blow-up, Perturbations of parameters, perturbations on the initial condition, stability, Perturbations, 517.98, Blow-up in context of PDEs, perturbations, https://purl.org/becyt/ford/1.1, https://purl.org/becyt/ford/1, Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs, Stability in context of PDEs, Semilinear parabolic equations, Stability, blow-up, perturbations of the domain, Blow-up rates, Perturbations on the initial condition, Análisis funcional y teoría de operadores
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