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Semilinear parabolic problems singularity non autonomous with critical exponents

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Author(s):
Marcelo Jose Dias Nascimento
Total Authors: 1
Document type: Doctoral Thesis
Press: São Carlos.
Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
Defense date:
Examining board members:
Alexandre Nolasco de Carvalho; Claudianor Oliveira Alves; Marcelo Moreira Cavalcanti; Ma To Fu; Antonio Luiz Pereira
Advisor: Alexandre Nolasco de Carvalho
Abstract

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] (AU)