On the stability of the standard Riemann semigroup

Authors:
Stefano Bianchini and Rinaldo M. Colombo

Journal:
Proc. Amer. Math. Soc. **130** (2002), 1961-1973

MSC (2000):
Primary 35L65, 76N10

DOI:
https://doi.org/10.1090/S0002-9939-02-06568-1

Published electronically:
February 27, 2002

MathSciNet review:
1896028

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Abstract | References | Similar Articles | Additional Information

Abstract: We consider the dependence of the entropic solution of a hyperbolic system of conservation laws

on the flux function . We prove that the solution is Lipschitz continuous w.r.t. the norm of the derivative of the perturbation of . We apply this result to prove the convergence of the solution of the relativistic Euler equation to the classical limit.

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Additional Information

**Stefano Bianchini**

Affiliation:
Istituto per le Applicazioni del Calcolo, Viale del Policlinico 137, 00161 Roma, Italy

Email:
bianchin@iac.rm.cnr.it

**Rinaldo M. Colombo**

Affiliation:
Department of Mathematics, University of Brescia, Via Valotti 9, 25133 Brescia, Italy

Email:
rinaldo@ing.unibs.it

DOI:
https://doi.org/10.1090/S0002-9939-02-06568-1

Keywords:
Hyperbolic systems,
conservation laws,
well posedness

Received by editor(s):
July 1, 2000

Published electronically:
February 27, 2002

Additional Notes:
We thank Alberto Bressan for useful discussions.

Communicated by:
Suncica Canic

Article copyright:
© Copyright 2002
American Mathematical Society