Existence and uniqueness for a nonlinear parabolic/Hamilton-Jacobi coupled system describing the dynamics of dislocation densities
Hassan Ibrahim (2009)
Annales de l'I.H.P. Analyse non linéaire
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Displaying similar documents to “A direct proof of the equivalence between the entropy solutions of conservation laws and viscosity solutions of Hamilton-Jacobi equations in one-space variable.”
Existence and uniqueness for a nonlinear parabolic/Hamilton-Jacobi coupled system describing the dynamics of dislocation densities
Entropy conditions and their numerical analogues for conservation laws
R. Ansorge (1994)
Banach Center Publications
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The minimum entropy principle for compressible fluid flows in a nozzle with discontinuous cross-section
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...
Obstacle problems for scalar conservation laws
Laurent Levi (2001)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In this paper we are interested in bilateral obstacle problems for quasilinear scalar conservation laws associated with Dirichlet boundary conditions. Firstly, we provide a suitable entropy formulation which ensures uniqueness. Then, we justify the existence of a solution through the method of penalization and by referring to the notion of entropy process solution due to specific properties of bounded sequences in . Lastly, we study the behaviour of this solution and its stability properties...