Title: Equilibrium-diffusion limit of the radiation model Show Chinese title

Title: 辐射模型的平衡扩散极限

Abstract: We justify rigorously the equilibrium-diffusion limit of the model consists of a radiative transfer satisfied by the specific intensity of radiation coupled to a diffusion equation satisfied by the material temperature. For general initial data, we construct the existence of the solution to the coupled model in $\mathbb{T}^{3}$ by the Hilbert expansion and prove the convergence of the solutions to the limiting system in the equilibrium-diffusion regime. Moreover, the initial layer for the radiative density and the temperature are constructed to get the strong convergence in $L^\infty$ norm. We also get the convergence rates about the intensity of radiation and temperature in this paper. Show Chinese abstract

Abstract: 我们严格推导了由满足辐射强度特定传输方程和材料温度扩散方程耦合组成的模型的平衡-扩散极限。 对于一般的初始数据，在 $\mathbb{T}^{3}$ 中通过希尔伯特展开构造了耦合模型解的存在性，并证明了解在平衡-扩散区域收敛到极限系统的性质。 此外，为了在 $L^\infty$ 范数下获得强收敛性，构建了辐射密度和温度的初始层。 本文还得到了关于辐射强度和温度的收敛率。