We consider the dependence of the entropic solution of a hyperbolic system of conservation laws {ut + f(u)x = 0, u(0, ·) = u0 on the flux function f. We prove that the solution is Lipschitz continuous w.r.t, the C0 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.
On the stability of the standard Riemann semigroup / Bianchini, S.; Colombo, R. M.. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 130:7(2002), pp. 1961-1973. [10.1090/S0002-9939-02-06568-1]
On the stability of the standard Riemann semigroup
Bianchini, S.;
2002-01-01
Abstract
We consider the dependence of the entropic solution of a hyperbolic system of conservation laws {ut + f(u)x = 0, u(0, ·) = u0 on the flux function f. We prove that the solution is Lipschitz continuous w.r.t, the C0 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.File in questo prodotto:
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