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MiS Preprint
44/2000
On the Stability of the Standard Riemann Semigroup
Stefano Bianchini and Rinaldo M. Colombo
Abstract
We consider the dependence of the entropic solution of a hyperbolic system of conservation laws $\left\{ \begin{array}{rcl} u_i =f(u)_x =0\\ u(0,\cdot ) =u_0 \end{array} \right\}$ 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.
