Uniqueness of entropy solutions for nonlinear degenerate parabolic problems

Mohamed Maliki () and Hamidou Touré ()
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Mohamed Maliki: Équipe: modélisation E.D.P. et Analyse numérique F.S.T. Mohammédia
Hamidou Touré: UFR/SEA Université de Ouagadougou

A chapter in Nonlinear Evolution Equations and Related Topics, 2004, pp 603-622 from Springer

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

Keywords: 35K65; 35L65; Parabolic equation; hyperbolic equation; weak solution; entropy solution (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-0348-7924-8_31

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DOI: 10.1007/978-3-0348-7924-8_31

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