250 citations · 1.1k across the 130 of their papers we have counts for
7 papers · 2 filters
Late-time/stiff relaxation asymptotic-preserving approximations of hyperbolic equations
Christophe Berthon, Philippe G. LeFloch, Rodolphe Turpault
We investigate the late-time asymptotic behavior of solutions to nonlinear hyperbolic systems of conservation laws containing stiff relaxation terms. First, we introduce a Chapman-…
Coupling techniques for nonlinear hyperbolic equations. I. Self-similar diffusion for thin interfaces
Benjamin Boutin, Frédéric Coquel, Philippe G. LeFloch
We investigate various analytical and numerical techniques for the coupling of nonlinear hyperbolic systems and, in particular, we introduce here an augmented formulation which all…
Hyperbolic conservation laws on spacetimes
Philippe G. LeFloch
We present a generalization of Kruzkov's theory to manifolds. Nonlinear hyperbolic conservation laws are posed on a differential (n+1)-manifold, called a spacetime, and the flux fi…
Why many theories of shock waves are necessary. Kinetic relations for nonconservative systems
Christophe Berthon, Frédéric Coquel, Philippe G. LeFloch
For a class of nonconservative hyperbolic systems of partial differential equations endowed with a strictly convex mathematical entropy, we formulate the initial value problem by s…
Existence and qualitative properties of kinetic functions generated by diffusive-dispersive regularizations
Philippe G. LeFloch
We investigate the properties of traveling wave solutions to hyperbolic conservation laws augmented with diffusion and dispersion, and review the existence and qualitative properti…
Kinetic relations for undercompressive shock waves. Physical, mathematical, and numerical issues
Philippe G. LeFloch
Kinetic relations are required in order to characterize nonclassical undercompressive shock waves and formulate a well-posed initial value problem for nonlinear hyperbolic systems…