Study of boundary conditions for a strictly hyperbolic system via the parabolic approximation. (Étude des conditions aux limites pour un système strictement hyperbolique via l’approximation parabolique.) (French. Abridged English version) Zbl 0808.35075

Gisclon, Marguerite; Serre, Denis

C. R. Acad. Sci., Paris, Sér. I 319, No. 4, 377-382 (1994).

Summary: We consider a hyperbolic system of conservation laws with boundary conditions in one space variable. We search the boundary conditions in order to have a well posed initial boundary value problem in the quarter plane \(x>0\), \(t>0\). We use the viscosity method; we study the solutions perturbed by a viscous term \(\varepsilon>0\) and in particular the behaviour of the boundary conditions as \(\varepsilon\) tends to zero.

MSC:

35L65	Hyperbolic conservation laws
35B40	Asymptotic behavior of solutions to PDEs

Keywords:

viscosity method