A note on the uniqueness of entropy solutions of nonlinear degenerate parabolic equations

By Kenneth Hvistendahl Karlsen, Mario Ohlberger. Journal of Mathematical Analysis and Applications, 2002

48 citations recorded by the source corpus.

Abstract Following the lead of [Carrillo, Arch. Ration. Mech. Anal. 147 (1999) 269–361], recently several authors have used Kružkov's device of “doubling the variables” to prove uniqueness results for entropy solutions of nonlinear degenerate parabolic equations. In all these results, the second order differential operator is not allowed to depend explicitly on the spatial variable, which certainly restricts the range of applications of entropy solution theory. The purpose of this paper is to extend a version of Carrillo's uniqueness result to a class of degenerate parabolic equations with spatially dependent second order differential operator. The class is large enough to encompass several interesting nonlinear partial differential equations coming from the theory of porous media flow and the phenomenological theory of sedimentation-consolidation processes.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/1999f64fb32e08db9b042ae0acf1a2f97b5734c0

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Citations in the corpus

Renormalized entropy solutions of homogeneous Dirichlet problems for quasilinear anisotropic degenerate parabolic-hyperbolic equations (2012, background): “Various extensions of his important result can be found in [11,23,24].”
QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC EQUATIONS WITH TIME-SPACE DEPENDENT DIFFUSION COEFFICIENTS (2005, methodology): “An exception is the work of Karlsen and Ohlberger [24], which treats (1.”