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On the continuation of solutions of non-autonomous semilinear parabolic problems

Part of: Partial differential equations Parabolic equations and systems

Published online by Cambridge University Press:  13 July 2015

Alexandre N. Carvalho ,
Jan W. Cholewa  and
Marcelo J. D. Nascimento
Alexandre N. Carvalho
Affiliation:
Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, Campus de São Carlos, Caixa Postal 668, 13560-970 São Carlos, São Paulo, Brazil (andcarva@icmc.usp.br)
Jan W. Cholewa
Affiliation:
Institute of Mathematics, Silesian University, 40-007 Katowice, Poland (jan.cholewa@us.edu.pl)
Marcelo J. D. Nascimento
Affiliation:
Departamento de Matemática, Universidade Federal de São Carlos, 13565-905 São Carlos, São Paulo, Brazil (marcelo@dm.ufscar.br)
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Abstract

We study non-autonomous parabolic equations with critical exponents in a scale of Banach spaces Eσ, σ ∈ [0,1 + μ). We consider a suitable E1+ε-solution and describe continuation properties of the solution. This concerns both a situation when the solution can be continued as an E1+ε-solution and a situation when the E1+ε-norm of the solution blows up, in which case a piecewise E1+ε-solution is constructed.

Keywords

abstract parabolic equationscontinuation of solutionscritical exponents

MSC classification

Secondary: 35K90: Abstract parabolic equations 35B60: Continuation and prolongation of solutions 35B33: Critical exponents
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 1 , February 2016 , pp. 17 - 55
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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