Semilinear parabolic problems singularity non autonomous with critical exponents

Author(s)

Marcelo Jose Dias Nascimento

• Document type: Doctoral Thesis
• Press: São Carlos.
• Institution: Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB)
• Defense date: 2007-02-15

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)