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Master's Dissertation
DOI
10.11606/D.45.2016.tde-15082012-231548
Document
Author
Full name
Luís Cláudio Yamaoka
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2006
Supervisor
Committee
Cordaro, Paulo Domingos (President)
Erazo, Oscar Fortunato Vilcachagua
Petronilho, Gerson
Title in Portuguese
Resolubilidade local de equações semilineares no plano
Keywords in Portuguese
Resolubilidade
Sistemas
Subdeterminados
Abstract in Portuguese
Seja Ω ⊂ ℝ2 aberto contendo a origem. Denotando as variáveis por (x,t), provamos a resolubilidade local, em um disco D aberto centrado na origem, D ⊂ Ω, de equações semilineares da forma Pu = f(x,t,u); onde P = ∂t + a(x,t)∂x, a ∈ C2 (Ω), Im ≠ 0 e f ∈ C2 (Ω × ℂ), usando o princípio da contração; P = ∂t - itkx, k: número inteiro positivo par e f ∈ C(ℝ2 × ℂ), usando o teorema da resolubilidade local de Hounie e Santiago.
Title in English
Local solvability of semilinear equations in the plane
Keywords in English
Solvability
Systems
Undetermined
Abstract in English
Let Ω be an open set of ℝ2 containing the origin. Using the variables (x,t), we prove the local solvability, on an open ball D centered at the origin, D ⊂ Ω, of semilinear equations of the form Pu = f(x,t,u); where P = ∂t + a(x,t)∂x, a ∈ C2 (Ω), Im ≠ 0 and f ∈ C2 (Ω × ℂ), using the principle of contracting mappings; P = ∂t - itkx, k: even positive integer number and f ∈ C(ℝ2 × ℂ), using the local solvability theorem of Hounie and Santiago.
 
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Publishing Date
2016-09-21
 
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