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Doctoral Thesis
DOI
10.11606/T.55.2003.tde-25042003-183522
Document
Author
Full name
Vera Lucia Carbone
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2003
Supervisor
Committee
Ruas Filho, Jose Gaspar (President)
Carvalho, Alexandre Nolasco de
Nascimento, Arnaldo Simal do
Oliva Filho, Sergio Muniz
Oliveira, Luiz Augusto Fernandes de
Title in Portuguese
Problemas parabólicos em materiais compostos unidimensionais: propriedade de Morse Smale.
Keywords in Portuguese
atratores e propriedade de Morse-Smale
transversalidade das variedades estável e instável
variedades invariantes
Abstract in Portuguese
Neste trabalho estudamos problemas de reação difusão em domínios unidimensionais que surgem de materiais compostos e obtemos resultados comparando os fluxos do problema original e do problema limite quando a difusão fica muito grande em partes do domínio. Provamos que os autovalores e autofunções do operador linear ilimitado associado à equação limite têm a propriedade de Sturm Liouville e provamos que as soluções do problema de reação difusão têm a propriedade do decrescimento do número de zeros ao longo do tempo. Estes resultados são usados para provar que as variedades instável e estável de pontos de equilíbrios são genericamente transversais e que o fluxo no atrator para o problema de reação difusão é genericamente estruturalmente estável. Estes fatos permitem obter a equivalência topológica dos fluxos restritos aos atratores dos problemas original e seu problema limite.
Title in English
Parabolic problems in unidimensional composite materials: Morse-Smale property.
Keywords in English
attractors and Morse-Smale property
invariant manifolds
transversality of he stable and unstable manifolds
Abstract in English
In this work we study some reaction-difusion problems in one dimensional domains that arise from composite materials. We obtain some results comparing the flux of the original problem and the flux of the limit problem when the difusion becomes large on parts of the physical domain. We prove that the eigenvalues and eigenfunctions of the linear unbounded operator associated with the equation have the Sturm Liouville property and also that the solutions of the reaction difusion equation have the property that the zeros do not increase with time. These results are used to obtain that the stable and unstable manifolds of equilibrium points are generically transversal and that the flux on the attractor for the reaction difusion problem is generically structurally stable. Using this we are able to prove the topological equivalence of the fluxs restricted to the attractors of the original and the limit problem.
 
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Publishing Date
2003-06-18
 
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