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Abstract:

We study small random perturbations by additive white-noise of a spatial discretization of a reaction-diffusion equation with a stable equilibrium and solutions that blow up in finite time. We prove that the perturbed system blows up with total probability and establish its order of magnitude and asymptotic distribution. For initial data in the domain of explosion we prove that the explosion time converges to the deterministic one while for initial data in the domain of attraction of the stable equilibrium we show that the system exhibits metastable behavior. © 2011 Elsevier Inc.

Registro:

Documento: Artículo
Título:Small random perturbations of a dynamical system with blow-up
Autor:Groisman, P.; Saglietti, S.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón I, Ciudad Universitaria, C1428EGA Buenos Aires, Argentina
Palabras clave:Blow-up; Explosions; Metastability; Random perturbations; Stochastic differential equations
Año:2012
Volumen:385
Número:1
Página de inicio:150
Página de fin:166
DOI: http://dx.doi.org/10.1016/j.jmaa.2011.06.034
Título revista:Journal of Mathematical Analysis and Applications
Título revista abreviado:J. Math. Anal. Appl.
ISSN:0022247X
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_0022247X_v385_n1_p150_Groisman.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0022247X_v385_n1_p150_Groisman

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Citas:

---------- APA ----------
Groisman, P. & Saglietti, S. (2012) . Small random perturbations of a dynamical system with blow-up. Journal of Mathematical Analysis and Applications, 385(1), 150-166.
http://dx.doi.org/10.1016/j.jmaa.2011.06.034
---------- CHICAGO ----------
Groisman, P., Saglietti, S. "Small random perturbations of a dynamical system with blow-up" . Journal of Mathematical Analysis and Applications 385, no. 1 (2012) : 150-166.
http://dx.doi.org/10.1016/j.jmaa.2011.06.034
---------- MLA ----------
Groisman, P., Saglietti, S. "Small random perturbations of a dynamical system with blow-up" . Journal of Mathematical Analysis and Applications, vol. 385, no. 1, 2012, pp. 150-166.
http://dx.doi.org/10.1016/j.jmaa.2011.06.034
---------- VANCOUVER ----------
Groisman, P., Saglietti, S. Small random perturbations of a dynamical system with blow-up. J. Math. Anal. Appl. 2012;385(1):150-166.
http://dx.doi.org/10.1016/j.jmaa.2011.06.034