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Doctoral Thesis
DOI
10.11606/T.55.2012.tde-13042012-162303
Document
Author
Full name
Éder Rítis Aragão Costa
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2012
Supervisor
Committee
Carvalho, Alexandre Nolasco de (President)
Martin, Luiz Antonio Barrera San
Rodrigues, Hildebrando Munhoz
Rosa, Ricardo Martins da Silva
Rosado, José Antonio Langa
Title in Portuguese
Sistemas gradientes, decomposição de Morse e funções de Lyapunov sob perturbação
Keywords in Portuguese
Atratores locais
Decomposição de Morse
Funções de Lyapunov
Processos de evolução de tipo gradiente
Semigrupos gradientes
Sistemas com acoplamento unilateral
Abstract in Portuguese
Neste trabalho investigamos a existência de uma função de Lyapunov associada a um sistema de tipo gradiente, semigrupos ou processos de evolução. Para isso, um estudo detalhado da teoria de Morse desempenha um papel decisivo. Como principal consequência deste estudo obtemos a estabilidade dos sistemas gradientes sob perturbação (autônoma ou não). A aplicabilidade dos resultados abstratos que aqui discutimos é exemplificada estudando-se sistemas de equações diferenciais em espaços de Banach com acoplamento unilateral
Title in English
Gradient systems, Morse decomposition and Lyapunov functions under pertubation
Keywords in English
Gradient semigroups
Gradient-like evolution processes
Local attractors
Lyapunov functions
Morse decomposition
Systems with unilateral coupling
Abstract in English
In this work we investigated the existence of a Lyapunov function associated to a gradient-like system, semigroups or evolution processes. For that, a detailed study of Morse theory plays a central role. As the main consequence of this study we obtain the stability of gradient systems under perturbation (autonomous or not). The applicability of the abstract results discussed here is exemplified by studying systems of differential equations in Banach spaces with unilateral coupling
 
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Publishing Date
2012-04-13
 
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