José Maria Arrieta | University of Texas at Austin - Estados Unidos
Existence, non-existence and concentration of solutions to some biharmonic problem...
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Author(s): |
Marcelo Jose Dias Nascimento
Total Authors: 1
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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
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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) |