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

DOI10.1007/s00526-013-0633-5zbMath1293.35149arXiv1208.0789OpenAlexW2040943537MaRDI QIDQ2248846

Daniel Matthes, Marco Di Francesco

Publication date: 27 June 2014

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.0789

zbMATH Keywords

gradient flow\(L^2\)-Wasserstein spaceinhomogeneous convectionJKO variational approximation scheme

Mathematics Subject Classification ID

Degenerate parabolic equations (35K65) Hyperbolic conservation laws (35L65) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

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Cites Work

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• Contractivity of Wasserstein metrics and asymptotic profiles for scalar conservation laws
• Entropy solutions for nonlinear degenerate problems
• On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients
• A note on the uniqueness of entropy solutions of nonlinear degenerate parabolic equations.
• Entropic Burgers' equation via a minimizing movement scheme based on the Wasserstein metric
• Polygonal approximations of solutions of the initial value problem for a conservation law
• The semigroup approach to first order quasilinear equations in several space variables
• The entropy rate admissibility criterion for solutions of hyperbolic conservation laws
• Eulerian Calculus for the Displacement Convexity in the Wasserstein Distance
• A Family of Nonlinear Fourth Order Equations of Gradient Flow Type
• GENERALIZED SOLUTIONS OF THE HAMILTON-JACOBI EQUATIONS OF EIKONAL TYPE. I. FORMULATION OF THE PROBLEMS; EXISTENCE, UNIQUENESS AND STABILITY THEOREMS; SOME PROPERTIES OF THE SOLUTIONS
• The Variational Formulation of the Fokker--Planck Equation
• CONTRACTIVE METRICS FOR SCALAR CONSERVATION LAWS
• Eulerian Calculus for the Contraction in the Wasserstein Distance
• FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES
• Optimal Transport