We consider a hyperbolic system of conservation laws where each characteristic field is either linearly degenerate or genuinely nonlinear. Under the assumption of coinciding shock and rarefaction curves and the existence of a set of Riemann coordinates w, w prove that there exists a semigroup of solutions u(t) = S(t)u(0), defined on initial data u(0) is an element of L-infinity. The semigroup S is continuous w.r.t. time and the initial data u(0) in the L-loc(1) topology. Moreover, S is unique and its trajectories are obtained as limits of wave front tracking approximations

Stability of L-infinity solutions for hyperbolic systems with coinciding shocks and rarefactions / Bianchini, Stefano. - In: SIAM JOURNAL ON MATHEMATICAL ANALYSIS. - ISSN 0036-1410. - 33:4(2001), pp. 959-981. [10.1137/S0036141000377900]

Stability of L-infinity solutions for hyperbolic systems with coinciding shocks and rarefactions

Bianchini, Stefano
2001-01-01

Abstract

We consider a hyperbolic system of conservation laws where each characteristic field is either linearly degenerate or genuinely nonlinear. Under the assumption of coinciding shock and rarefaction curves and the existence of a set of Riemann coordinates w, w prove that there exists a semigroup of solutions u(t) = S(t)u(0), defined on initial data u(0) is an element of L-infinity. The semigroup S is continuous w.r.t. time and the initial data u(0) in the L-loc(1) topology. Moreover, S is unique and its trajectories are obtained as limits of wave front tracking approximations
2001
33
4
959
981
https://arxiv.org/abs/math/0006094
Bianchini, Stefano
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/13711
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