Stability of shock waves for the Broadwell equations

Russel Caflisch, Tai Ping Liu

Research output: Contribution to journalArticle

Abstract

For the Broadwell model of the nonlinear Boltzmann equation, there are shock profile solutions, i.e. smooth traveling waves that connect two equilibrium states. For weak shock waves, we prove asymptotic (in time) stability with respect to small perturbations of the initial data. Following the work of Liu [7] on shock wave stability for viscous conservation laws, the method consists of analyzing the solution as the sum of a shock wave, a diffusive wave, a linear hyperbolic wave and an error term. The diffusive and linear hyperbolic waves are approximate solutions of the fluid dynamic equations corresponding to the Broadwell model. The error term is estimated using a variation of the energy estimates of Kawashima and Matsumura [6] and the characteristic energy method of Liu [7].

Original languageEnglish (US)
Pages (from-to)103-130
Number of pages28
JournalCommunications in Mathematical Physics
Volume114
Issue number1
DOIs
StatePublished - Mar 1988

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Shock Waves
shock waves
Error term
Viscous Conservation Laws
Characteristics Method
energy methods
Energy Estimates
Energy Method
Smooth Solution
fluid dynamics
Fluid Dynamics
conservation laws
Boltzmann Equation
Equilibrium State
Dynamic Equation
Small Perturbations
traveling waves
Traveling Wave
Shock
Nonlinear Equations

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

Cite this

Stability of shock waves for the Broadwell equations. / Caflisch, Russel; Liu, Tai Ping.

In: Communications in Mathematical Physics, Vol. 114, No. 1, 03.1988, p. 103-130.

Research output: Contribution to journalArticle

Caflisch, Russel ; Liu, Tai Ping. / Stability of shock waves for the Broadwell equations. In: Communications in Mathematical Physics. 1988 ; Vol. 114, No. 1. pp. 103-130.
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