Boundary condition for systems of hyperbolic conservation laws. (Condition à la limite pour un système de lois de conservation.) (French) Zbl 0634.35046

Dubois, François; Le Floch, Philippe

C. R. Acad. Sci., Paris, Sér. I 304, 75-78 (1987).

We propose a formulation of the boundary condition for non linear hyperbolic systems of conservation laws. It is based on the notion of Riemann problem and leads to a “well posed” problem. The equivalence with classical formulations is established for both linear and non convex scalar cases. The study of isentropic Euler equations gives a non trivial example which is graphically detailed.

MSC:

35L65	Hyperbolic conservation laws
35L50	Initial-boundary value problems for first-order hyperbolic systems
35A05	General existence and uniqueness theorems (PDE) (MSC2000)

Keywords:

boundary condition; systems of conservation laws; Riemann problem; well posed; non convex; isentropic Euler equations