DIFFUSION ASYMPTOTICS OF A STEADY COUPLED MODEL FOR RADIATIVE TRANSFER IN A UNIT BALL

doi:10.1007/s10473-025-0404-3

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (4): 1284-1306.doi: 10.1007/s10473-025-0404-3

DIFFUSION ASYMPTOTICS OF A STEADY COUPLED MODEL FOR RADIATIVE TRANSFER IN A UNIT BALL

Lei LI, Zhengce ZHANG^*

School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China

收稿日期:2024-04-08 修回日期:2024-08-17 出版日期:2025-10-10 发布日期:2025-10-10

DIFFUSION ASYMPTOTICS OF A STEADY COUPLED MODEL FOR RADIATIVE TRANSFER IN A UNIT BALL

Lei LI, Zhengce ZHANG^*

School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China

Received:2024-04-08 Revised:2024-08-17 Online:2025-10-10 Published:2025-10-10
Contact: ^*Zhengce ZHANG, E-mail: zhangzc@mail.xjtu.edu.cn
About author:Lei LI, E-mail: lileimathmatica@outlook.com

摘要/Abstract

摘要： We consider the diffusion asymptotics of a coupled model arising in radiative transfer in a unit ball in $\mathbb{R}^{3}$ with one-speed velocity. The model consists of a steady kinetic equation satisfied by the specific intensity of radiation coupled with a nonhomogeneous elliptic equation satisfied by the material temperature. For the $O(\epsilon)$ boundary data of the intensity of the radiation and the suitable small boundary data of the temperature, we prove the existence, uniqueness and the nonequilibrium diffusion limit of solutions to the boundary value problem for the coupled model.

关键词: radiative transfer, diffusion approximation, asymptotic analysis, unit ball

Abstract: We consider the diffusion asymptotics of a coupled model arising in radiative transfer in a unit ball in $\mathbb{R}^{3}$ with one-speed velocity. The model consists of a steady kinetic equation satisfied by the specific intensity of radiation coupled with a nonhomogeneous elliptic equation satisfied by the material temperature. For the $O(\epsilon)$ boundary data of the intensity of the radiation and the suitable small boundary data of the temperature, we prove the existence, uniqueness and the nonequilibrium diffusion limit of solutions to the boundary value problem for the coupled model.

Key words: radiative transfer, diffusion approximation, asymptotic analysis, unit ball

Lei LI, Zhengce ZHANG. DIFFUSION ASYMPTOTICS OF A STEADY COUPLED MODEL FOR RADIATIVE TRANSFER IN A UNIT BALL[J]. 数学物理学报(英文版), 2025, 45(4): 1284-1306.

Lei LI, Zhengce ZHANG. DIFFUSION ASYMPTOTICS OF A STEADY COUPLED MODEL FOR RADIATIVE TRANSFER IN A UNIT BALL[J]. Acta mathematica scientia,Series B, 2025, 45(4): 1284-1306.

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DIFFUSION ASYMPTOTICS OF A STEADY COUPLED MODEL FOR RADIATIVE TRANSFER IN A UNIT BALL

DIFFUSION ASYMPTOTICS OF A STEADY COUPLED MODEL FOR RADIATIVE TRANSFER IN A UNIT BALL

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