Equilibrium-diffusion limit of the radiation model

Lei Li

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arXiv · 2504.18094

Equilibrium-diffusion limit of the radiation model

Lei Li

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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.

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Lei Li. 2025-04-25. Equilibrium-diffusion limit of the radiation model. https://arxiv.org/abs/2504.18094

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