IUMJ

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

Authors: Wen-Ching Lien and Shih-Hsien Yu

Issue: Volume 57 (2008), Issue 4, 1501-1556

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 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.