Zhang Qiao-fu | Searcharxiv

arXiv2012

Multi-scale Analysis for Rosseland Equation with Small Periodic Oscillating Coefficients

Rosseland equation is one of the most popular models of the conduction-radiation coupled heat transfer in the thermal protection system. The well-posedness, the corresponding mathematical theory and the Multi-scale analysis method for the Rosseland-type equations with small periodic oscillating coefficients are concerned, which provides a theoretical basis for the Multi-scale computation of the conduction-radiation coupled heat transfer in an optically thick medium with a small periodic structure. The global well-posedness of the Rosseland-type (parabolic) equations is given in the first part. The corresponding solving algorithms and their convergence analysis are presented in the second part. In the third part we study the well-posedness and the second-order two-scale asymptotic expansion of the Rosseland-type (elliptic) equations with small periodic oscillating coefficients. The convergence analysis of the second-order two-scale asymptotic expansion is studied in the last part.

math.AP↗

arXiv2012

Divergence form nonlinear nonsmooth elliptic equations with locally arbitrary growth conditions and nonlinear maximal regularity

This is a simplification of our prior work on the existence theory for the Rosseland-type equations. Inspired by the Rosseland equation in the conduction-radiation coupled heat transfer, we use the locally arbitrary growth conditions instead of the common global restricted growth conditions. In the Lebesgue square integrable space, the solution to the linear elliptic equation depends continuously on the coefficients matrix. This is a simple version of the maximal regularity. There exists a fixed point for the linearized map (compact and continuous) in a closed convex set. We also consider the Galerkin method.

math.AP↗