Equilibrium-diffusion limit of the radiation model
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915258370621440 |
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| author | Li, Lei |
| author_facet | Li, Lei |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_18094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Equilibrium-diffusion limit of the radiation model Li, Lei Analysis of PDEs 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. |
| title | Equilibrium-diffusion limit of the radiation model |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2504.18094 |