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On the validity of the Picard algorithm for nonlinear parabolic equations

Published online by Cambridge University Press:  12 July 2007

Marco Cannone  and
Grzegorz Karch
Marco Cannone
Affiliation:
Laboratoire d'Analyse et de Mathématiques Appliquées, Université de Marne-la-Vallée, Cité Descartes-5, bd Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2, France (cannone@math.univ-mlv.fr)
Grzegorz Karch
Affiliation:
Instytut Matematyczny, Uniwersytet Wrocławski, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland and Institute of Mathematics, Polish Academy of Sciences, PO Box 21, ul. Sniadeckich 8, 00-956 Warszawa 10, Poland. (karch@math.uni.wroc.pl)
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Abstract

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We discuss some ill-posedness results for solutions arising from the Picard iterations algorithm (i.e. the Banach fixed-point theorem) in the case of the nonlinear heat equation, the viscous Hamilton–Jacobi equation, the convection–diffusion equation and the incompressible Navier–Stokes system.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 135 , Issue 5 , October 2005 , pp. 947 - 958
Copyright
Copyright © Royal Society of Edinburgh 2005