A note on the uniqueness of entropy solutions to first order quasilinear equations.
Diller, David J. (1994)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Diller, David J. (1994)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Florent Berthelin (2003)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We study in this paper some numerical schemes for hyperbolic systems with unilateral constraint. In particular, we deal with the scalar case, the isentropic gas dynamics system and the full-gas dynamics system. We prove the convergence of the scheme to an entropy solution of the isentropic gas dynamics with unilateral constraint on the density and mass loss. We also study the non-trivial steady states of the system.
R. Ansorge (1994)
Banach Center Publications
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Dietmar Kröner, Philippe G. LeFloch, Mai-Duc Thanh (2008)
ESAIM: Mathematical Modelling and Numerical Analysis
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We consider the Euler equations for compressible fluids in a nozzle whose cross-section is variable and may contain discontinuities. We view these equations as a hyperbolic system in nonconservative form and investigate weak solutions in the sense of Dal Maso, LeFloch and Murat [ (1995) 483–548]. Observing that the entropy equality has a fully conservative form, we derive a minimum entropy principle satisfied by entropy solutions. We then establish the stability of a...