论文标题
稳态辐射传热系统的扩散极限：边界层
Diffusive limits of the steady state radiative heat transfer system: Boundary layers
论文作者
论文摘要
在本文中，我们研究了具有平坦边界的有界域中的非均匀dirichlet边界条件的稳态辐射传热系统的扩散极限。使用渐近分析来构建复合近似解决方案，考虑到边界层。使用BANACH固定点定理证明了在扩散极限中与近似解决方案的收敛性。主要的困难在于椭圆形和动力传输方程之间的非线性耦合。为了克服这个问题，提出了一个光谱假设，以确保提出边界层的线性稳定性。此外，合并的$ l^2 $ - $ l^\ infty $估计和Banach固定点定理用于获得收敛证明。此结果将我们以前的工作\ cite {Ghattassi202020-Diffusive}对于已准备好的边界数据案例的{ghattassi20-Diffusive}，到存在边界层存在时，将其做好了准备。
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. A composite approximate solution is constructed using asymptotic analysis taking into account of the boundary layers. The convergence to the approximate solution in the diffusive limit is proved using a Banach fixed point theorem. The major difficulty lies on the nonlinear coupling between elliptic and kinetic transport equations. To overcome this problem, a spectral assumption ensuring the linear stability of the boundary layers is proposed. Moreover, a combined $L^2$-$L^\infty$ estimate and the Banach fixed point theorem are used to obtain the convergence proof. This results extend our previous work \cite{ghattassi2020diffusive} for the well-prepared boundary data case to the ill-prepared case when boundary layer exists.
