A Discrete Kinetic Approximation of Entropy Solutions to Multidimensional Scalar Conservation Laws
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TL;DR: In this article, a new relaxation approximation to scalar conservation laws in several space variables was presented by means of semilinear hyperbolic systems of equations with a finite number of velocities.
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About: This article is published in Journal of Differential Equations. The article was published on 20 Sep 1998. and is currently open access. The article focuses on the topics: Conservation law & Relaxation (approximation).
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Citations
Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).
TL;DR: To the best of our knowledge, there is only one application of mathematical modelling to face recognition as mentioned in this paper, and it is a face recognition problem that scarcely clamoured for attention before the computer age but, having surfaced, has attracted the attention of some fine minds.
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Construction of bgk models with a family of kinetic entropies for a given system of conservation laws
TL;DR: The BGK models that lead to this system in the hydrodynamic limit, and that are compatible with the whole family of entropies are characterized by a new characterization of Maxwellians as entropy minimizers that can take into account the simultaneous minimization problems corresponding to the family ofEntropies.
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Discrete Kinetic Schemes for Multidimensional Systems of Conservation Laws
TL;DR: Some numerical schemes for general multidimensional systems of conservation laws based on a class of discrete kinetic approximations based on the relaxation schemes by S. Jin and Z. Xin are presented.
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Basic Aspects of Hyperbolic Relaxation Systems
Wen-An Yong
- 01 Jan 2001
TL;DR: In this paper, a systematic consideration of hyperbolic systems of first-order partial differential equations with source terms divided by a small parameter e is presented, and several basic structural condi-tions aiming at the existence of a well-behaved limit as e tends to zero are identified.
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A kinetic equation with kinetic entropy functions for scalar conservation laws. Final report
Benoît Perthame,Eitan Tadmor +1 more
- 01 Jan 1990
TL;DR: In this article, a nonlinear kinetic equation is constructed and proved to be well-adapted to describe general multidimensional scalar conservation laws, in particular in epsilon -the microscopic scale.
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References
On the rate of convergence to equilibrium for a system of conservation laws with a relaxation term
Aslak Tveito,Ragnar Winther +1 more
TL;DR: In this article, a simple system of conservation laws with a strong relaxation term is analyzed and well-posedness of the Cauchy problem in the framework of bounded-total-variation (BV) solutions is proved.
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The mathematical theory of dilute gases
Carlo Cercignani,Reinhard Illner,Mario Pulvirenti +2 more
- 01 Jan 1994
TL;DR: In this article, the authors present rigorous mathematical results in the kinetic theory of a gas of hard spheres, including the Boltzmann equations, global existence theory, and the fluid-dynamical limits.
Convergence results for some conservation laws with reflux boundary condition and a relaxation term arising in chemical engineering
TL;DR: In this paper, a system of 2N semilinear transport equations with a boundary condition of imposed flux is considered, and it is shown that under some assumptions on the flux, the solution to this system converges to a solution to N quasilinearly equations, a solution which satisfies a set of entropy inequalities.