Proceedings of the American Mathematical Society

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ISSN 1088-6826(e) ISSN 0002-9939(p)

On the stability of the standard Riemann semigroup

Author(s): Stefano Bianchini; Rinaldo M. Colombo
Journal: Proc. Amer. Math. Soc. 130 (2002), 1961-1973.
MSC (2000): Primary 35L65, 76N10
Posted: 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

. 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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