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Dynamics of a class of ODEs via wavelets


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Author: Munhoz Rodrigues, Hildebrando
Caraballo Garrido, Tomás
Fuzeto Gameiro, Marcio
Department: Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico
Date: 2017-11
Published in: Communications on Pure and Applied Analysis, 16 (6), 2337-2355.
Document type: Article
Abstract: The objective of this paper is to study a perturbed linear hyperbolic differential equation. The first part of this work is dedicated to study perturbation of the equilibrium (special solution) of a perturbed hyperbolic system. On the second part we analyze the stable and the unstable manifolds of a perturbed semilinear differential equation. We assume that the perturbed forcing function belongs to an L2 class and that it is developed in a series of wavelets. Then we analyze the effect of this development on the special solution of the perturbed equation. Similar study is provided for the stable and unstable manifolds of this special solutions.
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DOI: 10.3934/cpaa.2017115

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