On the Stability of the Standard Riemann Semigroup

Abstract

We consider the dependence of the entropic solution of a hyperbolic system of conservation laws \[ \{\{array}{c} u_t + f(u)_x = 0 u(0,\cdot) = u_0 \{array} \] 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.

11 pages