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On the existence of weak solutions to the Cauchy problem for a class of quasilinear hyperbolic equations with a source term.

Filipa Caetano — 2004

Revista Matemática Complutense

Following the ideas of D. Serre and J. Shearer (1993), we prove in this paper the existence of a weak solution of the Cauchy problem for a given second order quasilinear hyperbolic equation.

A second order anti-diffusive Lagrange-remap scheme for two-component flows

Marie Billaud Friess; Benjamin Boutin; Filipa Caetano; Gloria Faccanoni; Samuel Kokh; Frédéric Lagoutière; Laurent Navoret — 2011

ESAIM: Proceedings

We build a non-dissipative second order algorithm for the approximate resolution of the one-dimensional Euler system of compressible gas dynamics with two components. The considered model was proposed in [1]. The algorithm is based on [8] which deals with a non-dissipative first order resolution in Lagrange-remap formalism. In the present paper we describe, in the same framework, an algorithm that is second order accurate in time and space, and that...

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