Preprint 2000-036

On the Stability of the Standard Riemann Semigroup

Abstract: We consider the dependence of the entropic solution of a hyperbolic system of conservation laws \[ \left\{ \begin{array}{c} u_t + f(u)_x = 0 \\ u(0,\cdot) = u_0 \end{array} \right. \] on the flux function $f$. We prove that the solution in 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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Author(s):

Stefano Bianchini, <bianchin@sissa.it>

Rinaldo M. Colombo, <rinaldo@ing.unibs.it>

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<bianchin@sissa.it> September 7 2000.