Curves of steepest descent are entropy solutions for a class of degenerate convection-diffusion equations

Marco Di Francesco, Daniel Matthes

Research output: Contribution to journalArticle

11 Citations (Scopus)
127 Downloads (Pure)

Abstract

We consider a nonlinear degenerate convection-diffusion equation with inhomogeneous convection and prove that its entropy solutions in the sense of Kruzkov are obtained as the - a posteriori unique - limit points of the JKO variational approximation scheme for an associated gradient flow in the $L^2$-Wasserstein space. The equation lacks the necessary convexity properties which would allow to deduce well-posedness of the initial value problem by the abstract theory of metric gradient flows. Instead, we prove the entropy inequality directly by variational methods and conclude uniqueness by doubling of the variables.
Original languageEnglish
Pages (from-to)199-230
Number of pages32
JournalCalculus of Variations and Partial Differential Equations
Volume50
Issue number1-2
Early online date18 May 2013
DOIs
Publication statusPublished - May 2014

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