CONTRACTIVE METRICS FOR SCALAR CONSERVATION LAWS

DOI10.1142/S0219891605000397zbMath1071.35081arXivmath/0504136OpenAlexW1988224607MaRDI QIDQ4680610

Grégoire Loeper, François Bolley, Yann Brenier

Publication date: 7 June 2005

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0504136

zbMATH Keywords

conservation lawsentropy solutionsWasserstein distancecontraction property

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Initial value problems for first-order hyperbolic systems (35L45)

Related Items (20)

Manifold Approximations via Transported Subspaces: Model Reduction for Transport-Dominated Problems ⋮ Euler-Poisson systems as action-minimizing paths in the Wasserstein space ⋮ \(L^{2}\) formulation of multidimensional scalar conservation laws ⋮ One-Dimensional Pressureless Gas Systems with/without Viscosity ⋮ On gradient flow and entropy solutions for nonlocal transport equations with nonlinear mobility ⋮ Contractivity of Wasserstein metrics and asymptotic profiles for scalar conservation laws ⋮ Transport distances for PDEs: the coupling method ⋮ Approximation of a simple Navier-Stokes model by monotonic rearrangement ⋮ Lipschitz metrics for a class of nonlinear wave equations ⋮ Well posedness for pressureless Euler system with a flocking dissipation in Wasserstein space ⋮ Displacement Interpolation Using Monotone Rearrangement ⋮ \(L^{2}\)-contraction for shock waves of scalar viscous conservation laws ⋮ Curves of steepest descent are entropy solutions for a class of degenerate convection-diffusion equations ⋮ A Lipschitz metric for the Hunter–Saxton equation ⋮ Measure solutions to a system of continuity equations driven by Newtonian nonlocal interactions ⋮ A multitype sticky particle construction of Wasserstein stable semigroups solving one-dimensional diagonal hyperbolic systems with large monotonic data ⋮ On uniqueness of solutions to conservation laws verifying a single entropy condition ⋮ Equivalence of gradient flows and entropy solutions for singular nonlocal interaction equations in 1D ⋮ Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit ⋮ Contractions in the 2-Wasserstein length space and thermalization of granular media

Cites Work

• Résolution d'équations d'évolution quasilinéaires en dimension N d'espace à l'aide d'équations linéaires en dimension \(N+1\)
• Sticky Particles and Scalar Conservation Laws

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