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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2000.tde-20210729-123029
Document
Author
Full name
Sandra Maria Zapata Yepes
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2000
Supervisor
Title in Portuguese
Propagação de singularidades para a equação da onda em variedades Lorentzianas: o teorema de Hörmander
Keywords in Portuguese
Análise Funcional
Operadores Integrais
Abstract in Portuguese
A análise microlocal tem servido como ferramenta no estudo das equações diferenciais parciais lineares e não lineares. Neste trabalho, são estudados alguns fatos gerais de operadores pseudo-diferenciais, operadores integrais de Fourier e construção da parametriz de um operador estritamente hiperbólico, aplicados na solução do problema de Cauchy para a equação da onda em variedades Lorentzianas. Também estudamos algumas caracterizações do conjunto frente de ondas permitindo uma análise mais completa das singularidades com a prova de uma versão simples do teorema devido a Hörmander sobre propagação de singularidades ao longo das bicaracterísticas nulas
Title in English
not available
Abstract in English
The microlocal analysis has served as a tool in the study of linear partial differential equations. In this work, we have studied some general facts of pseudo-differential operators, Fourier integral operators and construction of the parametrix of the strictly hiperbolic operators, this applies to the solution of the Cauchy problem for the wave front set that permits a more complete analysis of the singularities with the proof of the simplest version of the Hörmander's theorem on propagation of singularities along the null bicharacteristics
 
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Publishing Date
2021-07-29
 
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