Compactness of bounded quasientropy solutions to the system of equations of an isothermal gas.
Comparison of Some Solution Concepts for Linear First-order Hyperbolic Differential Equations With Non-smooth Coefficients
Conservation laws. I: Viscosity solutions.
Conservation laws on complex networks
Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients
We consider the initial value problem for degenerate viscous and inviscid scalar conservation laws where the flux function depends on the spatial location through a “rough” coefficient function . We show that the Engquist-Osher (and hence all monotone) finite difference approximations converge to the unique entropy solution of the governing equation if, among other demands, is in , thereby providing alternative (new) existence proofs for entropy solutions of degenerate convection-diffusion equations...
Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients
We consider the initial value problem for degenerate viscous and inviscid scalar conservation laws where the flux function depends on the spatial location through a "rough"coefficient function k(x). We show that the Engquist-Osher (and hence all monotone) finite difference approximations converge to the unique entropy solution of the governing equation if, among other demands, k' is in BV, thereby providing alternative (new) existence proofs for entropy solutions of degenerate convection-diffusion...
Development of singularities in solutions of a hyperbolic system.
Error estimate for the characteristic method involving Oldroyd derivative in a tensorial transport problem.
Error estimates for scalar conservation laws by a kinetic approach.
Existence and uniqueness of solutions of quasilinear hyperbolic systems of partial differential-functional equations
Existence d'ondes de raréfaction pour des écoulements isentropiques
Existence of global weak solutions to a symmetrically hyperbolic system with a source.
Existence of solutions to generalized von Foerster equations with functional dependence
We prove the existence of solutions to a differential-functional system which describes a wide class of multi-component populations dependent on their past time and state densities and on their total size. Using two different types of the Hale operator, we incorporate in this model classical von Foerster-type equations as well as delays (past time dependence) and integrals (e.g. influence of a group of species).
Explicit Finite Element Schemes for First Order Symmetric Hyperbolic Systems.
Extrapolation Applied to Certain Discretization Methods Solving the Initial Value Problem for Hyperbolic Differential Equations.
Finite volume schemes for multi-dimensional hyperbolic systems based on the use of bicharacteristics
In this paper we present recent results for the bicharacteristic based finite volume schemes, the so-called finite volume evolution Galerkin (FVEG) schemes. These methods were proposed to solve multi-dimensional hyperbolic conservation laws. They combine the usually conflicting design objectives of using the conservation form and following the characteristics, or bicharacteristics. This is realized by combining the finite volume formulation with approximate evolution operators, which use bicharacteristics...
Formes bilinéaires compatibles avec un système hyperbolique et problème de Cauchy
Generalized Solution to a Semilinear Hyperbolic System with a Non-Lipshitz Nonlinearity.
Generalized Solutions to Semilinear Hyperbolic Systems.
Genuinely multi-dimensional non-dissipative finite-volume schemes for transport
We develop a new multidimensional finite-volume algorithm for transport equations. This algorithm is both stable and non-dissipative. It is based on a reconstruction of the discrete solution inside each cell at every time step. The proposed reconstruction, which is genuinely multidimensional, allows recovering sharp profiles in both the direction of the transport velocity and the transverse direction. It constitutes an extension of the one-dimensional reconstructions analyzed in (Lagoutière, 2005;...