250 citations · 1.1k across the 130 of their papers we have counts for
10 papers · 2 filters
The Riemann problem for the shallow water equations with discontinuous topography
Philippe G. LeFloch, Mai-Duc Thanh
We construct the solution of the Riemann problem for the shallow water equations with discontinuous topography. The system under consideration is non-strictly hyperbolic and does n…
Zero diffusion-dispersion limits for scalar conservation laws
Cezar Kondo, Philippe G. LeFloch
We consider solutions of hyperbolic conservation laws regularized with vanishing diffusion and dispersion terms. Following a pioneering work by Schonbek, we establish the convergen…
Conservation laws with vanishing nonlinear diffusion and dispersion
Philippe G. LeFloch, Roberto Natalini
We study the limiting behavior of the solutions to a class of conservation laws with vanishing nonlinear diffusion and dispersion terms. We prove the convergence to the entropy sol…
Hyperbolic conservation laws and spacetimes with limited regularity
Philippe G. LeFloch
Hyperbolic conservation laws posed on manifolds arise in many applications to geophysical flows and general relativity. Recent work by the author and his collaborators attempts to…
Boundary layers in weak solutions to hyperbolic conservation laws
K. T. Joseph, Philippe G. LeFloch
This paper is concerned with the initial-boundary value problem for a nonlinear hyperbolic system of conservation laws. We study the boundary layers that may arise in approximation…
Propagating phase boundaries: formulation of the problem and existence via the Glimm scheme
Philippe G. LeFloch
In this paper we consider the hyperbolic-elliptic system of two conservation laws that describes the dynamics of an elastic material governed by a non-monotone strain-stress functi…