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 approximationsFile | Dimensione | Formato | |
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