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Doctoral Thesis
DOI
10.11606/T.55.2007.tde-09052007-104439
Document
Author
Full name
Marcelo Jose Dias Nascimento
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2007
Supervisor
Committee
Carvalho, Alexandre Nolasco de (President)
Alves, Claudianor Oliveira
Cavalcanti, Marcelo Moreira
Fu, Ma To
Pereira, Antonio Luiz
Title in Portuguese
Problemas parabólicos selineares singularmente não autônomos com expoentes críticos
Keywords in Portuguese
Continuação de soluções
Expoentes críticos
Problemas parabólicos
Soluções epsilon-regular
Abstract in Portuguese
Neste trabalho estudamos problemas de evolução da forma 'd ' úpsilond' SUP. ' úpsilon' t'' + A (t,'úpsilon' )' úpsilon' = f(t,'úpsilon' ) 'úpsilon'(0) = ' ' úpsilon' IND. 0' ', em um espaço de Banach X onde A(t, 'úpsilon' ) : D 'está contido em' X 'SETA ' X é um operador linear fechado e setorial para cada (t, ' úpsilon' ). Quando o operador A(t, ' úpsilon' ) é independente de ' úpsilon' , isto é, A(t, ' úpsilon') = A(t), mostramos um resultado de exitência, unicidade, continuidade relativamente a dados iniciais e continuação para o caso em que a não linearidade f tem crescimento crítico. Se A(t, 'úpsilon' ) depende do tempo e do estado, então mostramos um resultado de existência, unicidade com f tendo crescimento sub-crítico semelhante aos resultados encontrados em [7, 33]
Title in English
Semilinear parabolic problems singularity non autonomous with critical exponents
Keywords in English
Continuation of solutions
Critical expoents
Epsilon-regular solutions
Parabolic problems
Abstract in English
In this work we study initial value problems of the form ' d 'úpsilon' SUP. dt + A (t, 'úpsilon')'úpsilon' = f (t, 'úpsilon' ) ' úpsilon' (0) = ' úpsilon IND.0', in a Banach space X where A(t,' úpsilon' ) : D ' this contained ' X ' ARROW' X is an unbounded closed linear operator which is sectorial for each (t,' úpsilon' ). When the operator family A(t, ' úpsilon' ) is independent of ' úpsilon' , that is, A(t, ' úpsilon' ) = A(t), we show a result on local well posedness and continuation with the nonlinearity f growing critically. If A(t,' úpsilon' ) depends on the time t and on the state ' úpsilon' we show a local well posedness and continuation result that is similar to the result found in [7, 33]
 
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marcelo.pdf (809.30 Kbytes)
Publishing Date
2007-05-09
 
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