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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
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

\begin{displaymath}\left\{ \begin{array}{c} u_t + f(u)_x = 0, \\ u(0,\cdot) = u_0 \end{array} \right. \end{displaymath}

on the flux function $f$. We prove that the solution is Lipschitz continuous w.r.t. the $C^0$ norm of the derivative of the perturbation of $f$. 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

Rinaldo M. Colombo
Affiliation: Department of Mathematics, University of Brescia, Via Valotti 9, 25133 Brescia, Italy

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