Time-asymptotic interactions of Boltzmann shock layers in the presence of boundary

Wen Ching Lien, Shih Hsien Yu

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1 Citation (Scopus)

Abstract

We study the time-asymptotic behavior of the Boltzmann shock layers with a given physical boundary in a half-space. As boundary conditions, we prescribe a Maxwellian at the far field and require a specular reflection at the wall x = 0. When the macroscopic velocity at the far field is negative, we prove that if the initial data are suitably chosen, then a solution exists globally in time and tends toward the correspond-ing outgoing Boltzmann shock profile as time goes to infinity. The proof is essentially based on the macro-micro decomposition of solutions and the elementary energy methods.

Original languageEnglish
Pages (from-to)1501-1556
Number of pages56
JournalIndiana University Mathematics Journal
Volume57
Issue number4
DOIs
Publication statusPublished - 2008

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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