Global Regularity and Multiscale Approach for Thermal Radiation Heat Transfer
Jizu Huang, Liqun Cao · Multiscale Modeling and Simulation · 2014
This paper discusses the multiscale analysis for the thermal radiation heat transfer in composite materials with a periodic microstructure. The new contributions reported in this paper are threefold: global existence of the solution for the nonlinear equation with discontinuous coefficients is proved by using Rothe's method, the multiscale asymptotic expansions of the solution for the thermal radiation heat transfer equation with rapidly oscillating coefficients are presented, and the convergence results between the original solution $u^\varepsilon(x,t)$ and the multiscale asymptotic solutions with an explicit convergence rate are obtained.