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Uniqueness of entropy solutions for nonlinear degenerate parabolic problems

Uniqueness of entropy solutions for nonlinear degenerate parabolic problems We consider the general degenerate parabolic equation: $$ u_t - \Delta b(u) + div F(u) = f \quad \mathrm{in} \quad Q \in )0, T (\times \mathbb{R}^N, T > 0 $$ We prove existence of Kruzkhov entropy solutions of the associated Cauchy problem for bounded data where the flux function F is supposed to be continuous. Uniqueness is established under some additional assumptions on the modulus of continuity of F and b . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Evolution Equations Springer Journals

Uniqueness of entropy solutions for nonlinear degenerate parabolic problems

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References (12)

Publisher
Springer Journals
Copyright
Copyright © 2003 by Birkhäuser-Verlag
Subject
Mathematics
ISSN
1424-3199
eISSN
1424-3202
DOI
10.1007/s00028-003-0105-z
Publisher site
See Article on Publisher Site

Abstract

We consider the general degenerate parabolic equation: $$ u_t - \Delta b(u) + div F(u) = f \quad \mathrm{in} \quad Q \in )0, T (\times \mathbb{R}^N, T > 0 $$ We prove existence of Kruzkhov entropy solutions of the associated Cauchy problem for bounded data where the flux function F is supposed to be continuous. Uniqueness is established under some additional assumptions on the modulus of continuity of F and b .

Journal

Journal of Evolution Equations – Springer Journals

Published: Dec 1, 2003

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