Existence and uniqueness for a nonlinear parabolic/Hamilton-Jacobi coupled system describing the dynamics of dislocation densities

Hassan Ibrahim

Displaying similar documents to “Existence and uniqueness for a nonlinear parabolic/Hamilton-Jacobi coupled system describing the dynamics of dislocation densities”

A direct proof of the equivalence between the entropy solutions of conservation laws and viscosity solutions of Hamilton-Jacobi equations in one-space variable.

Aaibid, M., Sayah, A. (2006)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

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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 $L^{\infty}$ . Lastly, we study the behaviour of this solution and its stability properties...

Existence of $L^{\infty}$ entropy solutions for a reacting Euler system.

Gosse, L. (2001)

Portugaliae Mathematica. Nova Série

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Degenerate triply nonlinear problems with nonhomogeneous boundary conditions

Kaouther Ammar (2010)

Open Mathematics

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The paper addresses the existence and uniqueness of entropy solutions for the degenerate triply nonlinear problem: b(v)t − div α(v, ▽g(v)) = f on Q:= (0, T) × Ω with the initial condition b(v(0, ·)) = b(v 0) on Ω and the nonhomogeneous boundary condition “v = u” on some part of the boundary (0, T) × ∂Ω”. The function g is continuous locally Lipschitz continuous and has a flat region [A 1, A 2,] with A 1 ≤ 0 ≤ A 2 so that the problem is of parabolic-hyperbolic type.

Renormalized entropy solutions of scalar conservation laws

Philippe Bénilan, Jose Carrillo, Petra Wittbold (2000)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Well-posedness for non-isotropic degenerate parabolic-hyperbolic equations

Gui-Qiang Chen, Benoît Perthame (2003)

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Kinetic approach to systems of conservation laws

Benoît Perthame (1992)

Journées équations aux dérivées partielles

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Numerical flux-splitting for a class of hyperbolic systems with unilateral constraint

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.