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Doctoral Thesis
DOI
10.11606/T.55.2002.tde-23062015-142118
Document
Author
Full name
Katia Andreia Gonçalves de Azevedo
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2002
Supervisor
Committee
Ladeira, Luiz Augusto da Costa (President)
Oliva Filho, Sergio Muniz
Petronilho, Gerson
Santos, Jair Silverio dos
Táboas, Plácido Zoega
Title in Portuguese
Bifurcação de Hopf para uma classe de equações diferenciais parciais com retardamento
Keywords in Portuguese
Não disponível
Abstract in Portuguese
Neste trabalho nós estudamos a equação de reação difusão com retardamento {∂U/∂t (t,x) = ∂2U/∂x2(t, x) + kU(t,x) + k/δ ∫-r + δ-r g(U(t,x), U(t + s, x)ds, U(t, 0) = U(t, π) = 0, t≥0 U(t,x) = ψ(t, x), (t, x) ∈ [-r, 0] X [0, π]. Nós mostramos a existência de uma sequência de valores {Tkn}n= 0,1,2... do parâmetro τ tal que uma bifurcação de Hopf ocorre quando o retardo passa através de cada valor {Tkn}. As técnicas principais usadas aqui são alguns resultados sobre problemas de autovalor não lineares, a análise da equação característica do problema linearizado, o método de Liapunov-Schmidt e o Teorema da Função Implícita.
Title in English
Hopf bifurcation for a class of partial differential equation with delay
Keywords in English
Not available
Abstract in English
In this work we study the retarded reaction-diffusion equation {∂U/∂t (t,x) = ∂2U/∂x2(t, x) + kU(t,x) + k/δ ∫-r + δ-r g(U(t,x), U(t + s, x)ds, U(t, 0) = U(t, π) = 0, t≥0 U(t,x) = ψ(t, x), (t, x) ∈ [-r, 0] X [0, π]. We show the existence of a sequence of values {Tkn}n= 0,1,2... of the parameter T such that a Hopf bifurcation occurs when the delay passes through each value {Tkn}. The main techniques used here are some results on nonlinear eigenvalue problems, the analysis of the characteristic equation of the linearized problem, the Liapunov-Schmidt method and the Implicit Function Theorem.
 
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Publishing Date
2015-06-24
 
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