On a strong solution in the method of spherical harmonics for a nonstationary transport equation.
On an inequality in nonlinear thermoelasticity.
On continuous solutions to linear hyperbolic systems
We study the conditions under which the Cauchy problem for a linear hyperbolic system of partial differential equations of the first order in two independent variables has a unique continuous solution (not necessarily Lipschitz continuous). In addition to obvious continuity assumptions on coefficients and initial data, the sufficient conditions are the bounded variation of the left eigenvectors along the characteristic curves.
On -estimates for hyperbolic systems
On pseudosymmetric hyperbolic systems
On source terms and boundary conditions using arbitrary high order discontinuous Galerkin schemes
This article is devoted to the discretization of source terms and boundary conditions using discontinuous Galerkin schemes with an arbitrary high order of accuracy in space and time for the solution of hyperbolic conservation laws on unstructured triangular meshes. The building block of the method is a particular numerical flux function at the element interfaces based on the solution of Generalized Riemann Problems (GRPs) with piecewise polynomial initial data. The solution of the generalized Riemann...
On the boundary value problem in a dihedral angle for normally hyperbolic systems of first order.
On the characteristic initial value problem for nonlinear symmetric hyperbolic systems, including Einstein equations [Book]
On the existence and uniqueness of solutions of the Goursat problem for systems of functional partial differential equations of hyperbolic type.
On the existence of weak solutions for a semilinear singular hiperbolic system.
In this paper we prove the existence of a weak solution for a given semilinear singular real hyperbolic system.
On the motion of a body in thermal equilibrium immersed in a perfect gas
We consider a body immersed in a perfect gas and moving under the action of a constant force. Body and gas are in thermal equilibrium. We assume a stochastic interaction body/medium: when a particle of the medium hits the body, it is absorbed and immediately re-emitted with a Maxwellian distribution. This system gives rise to a microscopic model of friction. We study the approach of the body velocity V(t) to the limiting velocity and prove that, under suitable smallness assumptions, the approach...
On the well posedness of a system of balance laws with data
On the well-balance property of Roe’s method for nonconservative hyperbolic systems. Applications to shallow-water systems
This paper is concerned with the numerical approximations of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The first goal is to introduce a general concept of well-balancing for numerical schemes solving this kind of systems. Once this concept stated, we investigate the well-balance properties of numerical schemes based on the generalized Roe linearizations introduced by [Toumi, J. Comp. Phys. 102 (1992) 360–373]. Next, this general theory is applied to obtain well-balanced...
On the well-balance property of Roe's method for nonconservative hyperbolic systems. applications to shallow-water systems
This paper is concerned with the numerical approximations of Cauchy problems for one-dimensional nonconservative hyperbolic systems. The first goal is to introduce a general concept of well-balancing for numerical schemes solving this kind of systems. Once this concept stated, we investigate the well-balance properties of numerical schemes based on the generalized Roe linearizations introduced by [Toumi, J. Comp. Phys.102 (1992) 360–373]. Next, this general theory is applied to obtain well-balanced...
Ondes oscillantes simples quasilinéaires
One-dimensional adhesion model for large scale structures.
Optique Géométrique et invariance de jauge : Solutions oscillantes d’amplitude critique pour les équations de Yang-Mills