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Nonlinear Stability of Finite Volume Methods for Hyperbolic Conservation Laws: and Well-Balanced Schemes for Sources
Introduction.- 1. Quasilinear systems and conservation laws.- 2. Conservative schemes.- 3. Source terms.- 4. Nonconservative schemes.- 5. Multidimensional finite volumes with sources.- 6. NumericalExpand
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
A general strategy is described, based on a local hydrostatic reconstruction, that allows a well-balanced scheme to derive from any given numerical flux for the homogeneous problem, whenever the initial solver satisfies some classical stability properties. Expand
Hypoelliptic regularity in kinetic equations
Abstract We establish new regularity estimates, in terms of Sobolev spaces, of the solution f to a kinetic equation. The right-hand side can contain partial derivatives in time, space and velocity,Expand
Construction of BGK Models with a Family of Kinetic Entropies for a Given System of Conservation Laws
We introduce a general framework for kinetic BGK models. We assume to be given a system of hyperbolic conservation laws with a family of Lax entropies, and we characterize the BGK models that lead toExpand
One-dimensional transport equations with discontinuous coefficients
We consider one-dimensional linear transport equations with bounded but possibly discontinuous coefficient a. The Cauchy problem is studied from two different points of view. In the first case weExpand
Kruzkov's estimates for scalar conservation laws revisited
We give a synthetic statement of Kružkov-type estimates for multidimensional scalar conservation laws. We apply it to obtain various estimates for different approximation problems. In particular weExpand
Entropy satisfying flux vector splittings and kinetic BGK models
  • F. Bouchut
  • Mathematics, Computer Science
  • Numerische Mathematik
  • 1 June 2003
It is proved that the converse is true: any entropy fluxvector splitting can be interpreted by a kinetic model, and an explicit characterization of entropy satisfying flux vector splitting schemes is obtained. Expand
On long time asymptotics of the Vlasov-Fokker-Planck equation and of the Vlasov-Poisson-Fokker-Planck system with Coulombic and Newtonian potentials
We prove that the solution of the Vlasov-Fokker-Planck equation converges to the unique stationary solution with same mass as time tends to infinity. The same result holds in the repulsive coulombicExpand
Gravity driven shallow water models for arbitrary topography
Abstract. We derive new models for gravity driven shallow water flows in several space dimensions over a general topography. A first model is valid for small slope variation, i.e. small curvature,Expand