Preprint 2002-055

Asymptotic Stability of Riemann Solutions for a Class of Multi-D Viscous Systems of Conservation Laws

Hermano Frid

Abstract: We prove the asymptotic stability of two-states nonplanar Riemann solutions under initial and viscous perturbations for a class of multidimensional systems of conservation laws. The class of systems to which our result applies is constituted by those systems whose flux-functions in different directions share a common complete system of Riemann invariants, the level surfaces of which are hyperplanes. In particular, we obtain the uniqueness of the self-similar $L^\infty$ entropy solution of the two-states nonplanar Riemann problem. The asymptotic stability to which the main result refers is in the sense of the convergence as $t\to\infty$ in $L_{\loc}^1$ of the space of directions $\xix=\xx/t$. That is, the solution $u(t,\xx)$ of the perturbed problem satisfies $u(t,t\xix)\to R(\xix)$ as $t\to\infty$, in $L_{\loc}^1(\R^n)$, where $R(\xix)$ is the self-similar entropy solution of the corresponding two-states nonplanar Riemann problem.

Available as PostScript (320 Kbytes) or gzipped PostScript (128 Kbytes; uncompress using gunzip).
Hermano Frid, <>
Publishing information:
Submitted by:
<> December 17 2002.

[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | All Preprints | Preprint Server Homepage ]
© The copyright for the following documents lies with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use.

Conservation Laws Preprint Server <>
Last modified: Wed Dec 18 09:20:49 MET 2002