Journal title
Annales De L Institut Henri Poincare C Analyse Non Lineaire
DOI
10.1016/S0294-1449(02)00014-8
Issue
4
Volume
20
Last updated
2025-08-06T02:22:51.233+01:00
Page
645-668
Abstract
We develop a well-posedness theory for solutions in L<sup>1</sup> to the Cauchy problem of general degenerate parabolic-hyperbolic equations with non-isotropic nonlinearity. A new notion of entropy and kinetic solutions and a corresponding kinetic formulation are developed which extends the hyperbolic case. The notion of kinetic solutions applies to more general situations than that of entropy solutions; and its advantage is that the kinetic equations in the kinetic formulation are well defined even when the macroscopic fluxes are not locally integrable, so that L<sup>1</sup> is a natural space on which the kinetic solutions are posed. Based on this notion, we develop a new, simpler, more effective approach to prove the contraction property of kinetic solutions in L<sup>1</sup>, especially including entropy solutions. It includes a new ingredient, a chain rule type condition, which makes it different from the isotropic case. © 2003 Éditions scientifiques et médicales Elsevier SAS.
Symplectic ID
203199
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Publication type
Journal Article
Publication date
01 Jan 2003