Wave front tracking in systems of conservation laws
This paper contains several recent results about nonlinear systems of hyperbolic conservation laws obtained through the technique of Wave Front Tracking.
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Weak entropic solution to a scalar hyperbolic-parabolic law.
Guy Vallet (2003)
RACSAM
In this paper we are interested in the Dirichlet problem of a hyperbolic-parabolic degenerate equation. Thanks to a global entropic formulation in the sense of F. Otto, we propose a result of existence and uniqueness of the entropic measure valued solution and of the entropic weak solution in the space DM2.
Weak solutions for a hyperbolic system with unilateral constraint and mass loss
F Berthelin, F Bouchut (2003)
Annales de l'I.H.P. Analyse non linéaire
Weak solutions to the one-dimensional non-isentropic gas dynamics by the vanishing viscosity method.
Ito, Kazufumi (1996)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Weakly stable multidimensional shocks
Jean-François Coulombel (2004)
Annales de l'I.H.P. Analyse non linéaire
Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
Steve Bryson, Yekaterina Epshteyn, Alexander Kurganov, Guergana Petrova (2011)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves “lake at rest” steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples.
Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
Steve Bryson, Yekaterina Epshteyn, Alexander Kurganov, Guergana Petrova (2011)
ESAIM: Mathematical Modelling and Numerical Analysis
We introduce a new second-order central-upwind scheme for the Saint-Venant system of shallow water equations on triangular grids. We prove that the scheme both preserves “lake at rest” steady states and guarantees the positivity of the computed fluid depth. Moreover, it can be applied to models with discontinuous bottom topography and irregular channel widths. We demonstrate these features of the new scheme, as well as its high resolution and robustness in a number of numerical examples.
Well-posedness theory for geometry-compatible hyperbolic conservation laws on manifolds
Matania Ben-Artzi, Philippe G. Le Floch (2007)
Annales de l'I.H.P. Analyse non linéaire
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