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On the Stability of the Standard Riemann Semigroup

Stefano Bianchini·Rinaldo M. Colombo
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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.

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Stefano Bianchini, Rinaldo M. Colombo. 2000-07-10. On the Stability of the Standard Riemann Semigroup. https://arxiv.org/abs/math/0007055

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