Stationary solutions to the boundary value problem for the relativistic BGK model in a slab

Byung-Hoon Hwang; Seok-Bae Yun

doi:10.3934/krm.2019029

Article Contents

2019, Volume 12, Issue 4: 749-764. Doi: 10.3934/krm.2019029

This issue Previous Article Diffusion limit for kinetic Fokker-Planck equation with heavy tails equilibria: The critical case Next Article Effect of abrupt change of the wall temperature in the kinetic theory

Stationary solutions to the boundary value problem for the relativistic BGK model in a slab

Byung-Hoon Hwang and
Seok-Bae Yun^,

Department of Mathematics, Sungkyunkwan University, Suwon 440-746, Republic of Korea

^* Corresponding author: Seok-Bae Yun
^* Corresponding author: Seok-Bae Yun

Received: March 31, 2018

Revised: January 31, 2019

Published: May 2019

Seok-Bae Yun is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1B03935955).

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Abstract

In this paper, we are concerned with the boundary value problem in a slab for the stationary relativistic BGK model of Marle type, which is a relaxation model of the relativistic Boltzmann equation. In the case of fixed inflow boundary conditions, we establish the existence of unique stationary solutions.

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Mathematics Subject Classification: Primary: 35Q20, 76P05, 34K21, 35Q75, 83A05.

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