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Stabilization of oscillations in a phase transition model


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Opened Access Stabilization of oscillations in a phase transition model

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Author: Caraballo Garrido, Tomás
Colucci, Renato
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2017-02
Published in: Mathematical Methods in the Applied Sciences, 40 (3), 823-832.
Document type: Article
Abstract: In this paper we analyze a model presenting formation of microstructure depending on the parameters and the initial data. In particular we investigate how the presence of stochastic perturbations affects this phenomenon in its asymptotic behavior. Two different sufficient conditions are provided in order to prevent the formation of microstructure: the first one for Stratonovich’s noise while the second for Itˆo’s noise. The main contribution of the paper is that these conditions are independent of the initial values unlike in the deterministic model. Thus, we can interpret our results as some kind of stabilization produced by both types of noise.
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DOI: 10.1002/mma.4020

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