THE HIGH FIELD ASYMPTOTICS FOR A FERMIONIC BOLTZMANN EQUATION: ENTROPY SOLUTIONS AND KINETIC SHOCK PROFILES-Reference-Cited by-同舟云学术

THE HIGH FIELD ASYMPTOTICS FOR A FERMIONIC BOLTZMANN EQUATION: ENTROPY SOLUTIONS AND KINETIC SHOCK PROFILES

Published:2007-12 Issue:04 Volume:04 Page:679-704
ISSN:0219-8916
Container-title:Journal of Hyperbolic Differential Equations
language:en
Short-container-title:J. Hyper. Differential Equations

Author:

BEN ABDALLAH NAOUFEL¹,CHAKER HEDIA²,SCHMEISER CHRISTIAN³

Affiliation:

1. Institut de Mathématiques de Toulouse, Unité Mixte de Recherche 5219 (CNRS), Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France

2. Laboratoire de Modélisation et Simulation Numérique, dans les Sciences de l'INgénieurs, Ecole Nationale d'Ingénieurs de Tunis, BP 37, Campus Universitaire, Le Belvédère, 1002, Tunis, Tunisie

3. Faculty of Mathematics, University of Vienna, Nordbergstraße 15, 1090 Wien, Austria

Abstract

The high field approximation of a fermionic Boltzmann equation of semiconductors is performed after the formation of shocks. By employing a new entropy, whose dissipation measures the departure from the high field equilibrium, convergence towards the entropic solution of the limiting conservation law is proven. The entropy is also used to construct kinetic shock profiles for entropic shocks and to prove non-existence of non-entropic shock profiles.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics,Analysis

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219891607001318

Reference31 articles.

1. RUNAWAY PARTICLES FOR A BOLTZMANN-LIKE TRANSPORT EQUATION

2. THE HIGH FIELD ASYMPTOTICS FOR DEGENERATE SEMICONDUCTORS

3. High field approximations of the spherical harmonics expansion model for semiconductors

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