250 citations · 1.1k across the 130 of their papers we have counts for
4 papers · 2 filters
Singular limits in phase dynamics with physical viscosity and capillarity
K. T. Joseph, Philippe G. LeFloch
Following pioneering work by Fan and Slemrod who studied the effect of artificial viscosity terms, we consider the system of conservation laws arising in liquid-vapor phase dynamic…
Injectivity Radius of Lorentzian Manifolds
Bing-Long Chen, Philippe G. LeFloch
Motivated by the application to spacetimes of general relativity we investigate the geometry and regularity of Lorentzian manifolds under certain curvature and volume bounds. We es…
Hyperbolic Conservation Laws on Manifolds. Total Variation Estimates and the Finite Volume Method
Paulo Amorim, Matania Ben-Artzi, Philippe G. LeFloch
This paper investigates some properties of entropy solutions of hyperbolic conservation laws on a Riemannian manifold. First, we generalize the Total Variation Diminishing (TVD) pr…
Well-posedness theory for geometry compatible hyperbolic conservation laws on manifolds
Matania Ben-Artzi, Philippe G. LeFloch
Motivated by many applications (geophysical flows, general relativity), we attempt to set the foundations for a study of entropy solutions to nonlinear hyperbolic conservation laws…