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Master's Dissertation
DOI
10.11606/D.55.2018.tde-19012018-164402
Document
Author
Full name
Daniel Wellichan Mancini
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2001
Supervisor
Committee
Ruas Filho, Jose Gaspar (President)
Bergamasco, Adalberto Panobianco
Carvalho, Alexandre Nolasco de
Title in Portuguese
Propriedades genéricas de equilíbrios de equações parabólicas
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Nesta dissertação estudaremos a hiperbolicidade genérica dos equilíbrios de equações parabólicas da forma ut = Δu+ f(x,u,∇), > O, x ∈ Ω u = 0, > 0, x ∈ ∂Ω. Primeiramente, fixada uma função suave f, mostraremos que todos os seus equilíbrios são hiperbólicos quando a região Ω percorre um conjunto residual de uma classe de domínios regulares. Depois, fixada uma região regular Ω, suporemos que f independe de ∇u e provaremos que todos os equilíbrios são hiperbólicos quando f varia em um subconjunto residual de um conjunto de funções suficientemente regulares. Para a obtenção destes dois resultados utilizamos uma generalização, obtida por D. Henry, do Teorema da Transversalidade, cuja demonstração apresentamos neste trabalho.
Title in English
Not available
Keywords in English
Not available
Abstract in English
In this dissertaton we study the generic hyperbolicity of the equilibria of parabolic equations in the form Ut = Δu+f(x,u, ∇u), t > 0, x ∈ Ω u = 0, t > 0, x ∈ ∂Ω. First, we fix a smooth function f and show that ali equilibria of this equation are hyperbolic when the domam Ω runs over a residual set in a certain class of regular domains. Then, we fix a region Ω and, supposing that f does not depend on ∇u, we proof that ali equilibria are hyperbolic when f belongs to a residual subset in a set of sufficiently smooth functions. To obtain these two results we use a generalization, due to D. Henry, of the Transversality Theorem, whose proof we present in this work.
 
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Publishing Date
2018-01-22
 
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