论文标题
在辐射传热系统的扩散极限上I：准备充分的初始条件和边界条件
On the diffusive limits of radiative heat transfer system I: well prepared initial and boundary conditions
论文作者
论文摘要
我们研究了玻璃冷却，温室效应和天体物理学的非线性辐射传热系统的扩散极限近似。使用辐射强度的反射辐射边界条件以及温度的周期性，差异和罗宾边界条件来考虑该模型。该系统的全球存在是通过使用仔细处理边界条件处理的盖尔金方法给出的。使用紧凑型方法，平均引理和年轻度量理论，我们证明了我们的主要结果，即弱解决方案在扩散极限下会收敛到非线性扩散模型。此外，在限制系统上更规律的条件下，还通过使用相对熵方法来分析扩散极限。特别是，我们获得了收敛速度。从不存在初始和边界层的意义上说，初始条件和边界条件被假定为充分的准备。
We study the diffusive limit approximation for a nonlinear radiative heat transfer system that arises in the modeling of glass cooling, greenhouse effects and in astrophysics. The model is considered with the reflective radiative boundary conditions for the radiative intensity, and periodic, Dirichlet and Robin boundary conditions for the temperature. The global existence of weak solutions for this system is given by using a Galerkin method with a careful treatment of the boundary conditions. Using the compactness method, averaging lemma and Young measure theory, we prove our main result that the weak solution converges to a nonlinear diffusion model in the diffusive limit. Moreover, under more regularity conditions on the limit system, the diffusive limit is also analyzed by using a relative entropy method. In particular, we get a rate of convergence. The initial and boundary conditions are assumed to be well-prepared in the sense that no initial and boundary layer exist.
