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Master's Dissertation
DOI
Document
Author
Full name
Patricia Neves de Araujo
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2019
Supervisor
Committee
Pereira, Marcone Corrêa (President)
Gomez, Silvia Sastre
Pereira, Antonio Luiz
Title in Portuguese
Comportamento assintótico de problemas de difusão não locais e semilineares do tipo Neumann
Keywords in Portuguese
Blow-up
Comportamento assintótico
Equações não locais
Problemas do tipo Neumann
Abstract in Portuguese
Neste trabalho abordamos dois exemplos de equações de difusão não locais do tipo Neumann: o problema linear homogêneo e um semilinear com termo de reação representado pela função f(u) = u|u|^(p-1). Em ambos os casos, apresentamos condições de existência e unicidade de soluções e analisamos seu comportamento em relação ao tempo. Estudamos uma discretização para o problema linear e a utilizamos para realizar simulações numéricas nas quais podemos verificar algumas das propriedades demonstradas. Também simulamos o problema semilinear observando o comportamento de suas soluções mesmo em casos em que as hipóteses dos teoremas apresentados não são todas satisfeitas.
Title in English
Asymptotic behavior of nonlocal and semilinear diffusion problems of Neumann type
Keywords in English
Asymptotic behavior
Blow-up
Nonlocal equations
Problems of Neumann type
Abstract in English
In this work we approach two examples of nonlocal diffusion equations of Neumann type: the homogeneous linear problem and a semilinear with a reaction term represented by the function f(u) = u|u|^(p-1). In both cases, we present conditions of existence and uniqueness of solutions and we analyze their behavior with respect to time. We study a discretization to the linear problem and use it to perform numerical experiments in order to illustrate some of the demonstrated properties. We also simulate the semilinear problem observing the behavior of its solutions even in cases where the hypothesis of the presented theorems are not all satisfied.
 
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versaofinal.pdf (1.63 Mbytes)
Publishing Date
2019-09-03
 
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