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

• Autores: Wen-Ching Lien, Shih-Hsien Yu
• Localización: Indiana university mathematics journal, ISSN 0022-2518, Vol. 57, Nº 4, 2008, págs. 1501-1556
• Idioma: inglés
• DOI: 10.1512/iumj.2008.57.3262
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• Resumen

  • 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 corresponding 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.