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Abstract:

We study random perturbations of a reaction–diffusion equation with a unique stable equilibrium and solutions that blow-up in finite time. If the strength of the perturbation ε>0 is small and the initial data is in the domain of attraction of the stable equilibrium, the system exhibits metastable behavior: its time averages remain stable around this equilibrium until an abrupt and unpredictable transition occurs which leads to explosion in a finite time (but exponentially large in ε −2 ). Moreover, for initial data in the domain of explosion we show that the explosion times converge to the one of the deterministic solution. © 2017 Elsevier B.V.

Registro:

Documento: Artículo
Título:Metastability for small random perturbations of a PDE with blow-up
Autor:Groisman, P.; Saglietti, S.; Saintier, N.
Filiación:Departamento de Matemática, FCEN, Universidad de Buenos Aires, IMAS-CONICET, Argentina
NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai, China
Faculty of Industrial Engineering and Management, Technion, Israel
Palabras clave:Blow-up; Metastability; Random perturbations; Stochastic partial differential equations; Partial differential equations; Random processes; Stochastic systems; Blow-up; Domain of attraction; Metastabilities; Random perturbations; Reaction diffusion equations; Stable equilibrium; Stochastic partial differential equation; Time averages; Linear equations
Año:2018
Volumen:128
Número:5
Página de inicio:1558
Página de fin:1589
DOI: http://dx.doi.org/10.1016/j.spa.2017.08.005
Título revista:Stochastic Processes and their Applications
Título revista abreviado:Stoch. Processes Appl.
ISSN:03044149
CODEN:STOPB
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03044149_v128_n5_p1558_Groisman

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Citas:

---------- APA ----------
Groisman, P., Saglietti, S. & Saintier, N. (2018) . Metastability for small random perturbations of a PDE with blow-up. Stochastic Processes and their Applications, 128(5), 1558-1589.
http://dx.doi.org/10.1016/j.spa.2017.08.005
---------- CHICAGO ----------
Groisman, P., Saglietti, S., Saintier, N. "Metastability for small random perturbations of a PDE with blow-up" . Stochastic Processes and their Applications 128, no. 5 (2018) : 1558-1589.
http://dx.doi.org/10.1016/j.spa.2017.08.005
---------- MLA ----------
Groisman, P., Saglietti, S., Saintier, N. "Metastability for small random perturbations of a PDE with blow-up" . Stochastic Processes and their Applications, vol. 128, no. 5, 2018, pp. 1558-1589.
http://dx.doi.org/10.1016/j.spa.2017.08.005
---------- VANCOUVER ----------
Groisman, P., Saglietti, S., Saintier, N. Metastability for small random perturbations of a PDE with blow-up. Stoch. Processes Appl. 2018;128(5):1558-1589.
http://dx.doi.org/10.1016/j.spa.2017.08.005