Diffusive limits of the steady state radiative heat transfer system: Boundary layers

Mohamed Ghattassi, Xiaokai Huo, Nader Masmoudi

Research output: Contribution to journalArticlepeer-review


In this paper, we study the diffusive limit of the steady state radiative heat transfer system for non-homogeneous Dirichlet boundary conditions in a bounded domain with flat boundaries. By taking account of the boundary layers, a composite approximate solution is constructed using asymptotic analysis. The convergence to the composite approximate solution in the diffusive limit is proved using a Banach fixed point theorem. The major difficulty lies in the nonlinear coupling between elliptic and kinetic transport equations. To overcome this difficulty, a spectral assumption is proposed to ensure the linear stability of boundary layers. Moreover, a combined L2-L estimate and the Banach fixed point theorem are used to obtain the convergence proof. This result extends our previous work [6] for the well-prepared boundary data case to the general boundary date.

Original languageEnglish (US)
Pages (from-to)181-215
Number of pages35
JournalJournal des Mathematiques Pures et Appliquees
StatePublished - Jul 2023


  • Boundary layer
  • Diffusive limits
  • Milne problem
  • Radiative transfer system

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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