Nonlinear stability of the initial-boundary value problem for the broadwell model around a Maxwellian

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Abstract

We study the nonlinear stability of the equilibrium state associated with the initial boundary value problem for the Broadwell model with transonic boundary. Based on the Green's function of this linearized initial boundary value problem and on the understanding of its action on microscopic data, we establish the pointwise convergence of the solution toward the equilibrium state under small perturbation, via a solution representation and Picard-like iterations.

Original languageEnglish
Pages (from-to)131-157
Number of pages27
JournalJournal of Hyperbolic Differential Equations
Volume8
Issue number1
DOIs
Publication statusPublished - 2011 Mar 1

Keywords

  • Green's function
  • Initial boundary value problem
  • nonlinear stability

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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