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Doctoral Thesis
DOI
10.11606/T.55.2013.tde-06062013-145531
Document
Author
Full name
Paulo Mendes de Carvalho Neto
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2013
Supervisor
Committee
Carvalho, Alexandre Nolasco de (President)
Planas, Gabriela Del Valle
Rosado, José Antonio Langa
Rubio, Pedro Marin
Santos, Bruno Luis de Andrade
Title in English
Fractional differential equations: a novel study of local and global solutions in Banach spaces
Keywords in English
Fractional differential equations
Functional analysis
Mittag-Leffler functions
Partial differential equations
Abstract in English
Motivated by the huge success of the applications of the abstract fractional equations in many areas of science and engineering, and by the unsolved question in this theory, in this work we study several matters related to abstract fractional Cauchy problems of order 'alpha' 'it belongs' (0, 1). We search to answer some questions that were open: for instance, we analyze the existence of local mild solutions for the problem, and its possible continuation to a maximal interval of existence. The case of critical nonlinearities and corresponding regular mild solutions is also studied. Finally, by establishing some general comparison results, we apply them to conclude the global well-posedness of a fractional partial differential equation coming from heat conduction theory
Title in Portuguese
Equações diferenciais fracionárias: um novo estudo de soluções locais e globais em espaços de Banach
Keywords in Portuguese
Análise funcional
Equações diferenciais fracionárias
Equações diferenciais parciais
Funções de Mittag-Leffler
Abstract in Portuguese
Motivados pelo êxito das aplicações nas equações abstratas em muitas áreas da ciência e da engenharia, e pelas perguntas ainda abertas, neste trabalho estudamos questões relativas aos problemas fracionários abstratos de Cauchy de ordem 'alpha' 'pertence a' (0, 1). Buscamos responder algumas perguntas: por exemplo, analisamos a existência de soluções locais fracas do problema e sua possível continuação em um intervalo maximal de existência. O caso da não-linearidade crítica e sua correspondente solução regular fraca também é abordado. Por último, mediante o estabelecimento de alguns resultados gerais de comparação, chegamos a conclusão de que as soluções de uma equação diferencial parcial fracionária, proveniente da teoria de condução de calor, existe globalmente
 
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manuscript.pdf (2.66 Mbytes)
Publishing Date
2013-06-06
 
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