一类稳态扩散问题的死核估计

Dead Core Estimate of a Steady-State Diffusion Problem

考察了一类在化学反应研究中的具有Robin边界条件的非线性稳态扩散问题 ,由于扮演重要角色的死核边界是先验未知的 ,即这是一个自由边界问题 ,首先借助相应Dirichlet问题的解结合极值原理和比较原理 ,导出了该问题边值的上界和下界 ,说明死核是存在的 ,随后利用解在边界上的上、下界 ,估计了一般区域上死核所在的位置及其形状 。

The nonlinear steady state diffusion problem subject to Robin boundary condition is investigated. Such problems occur, for instance, in the study of chemical reactions. In such concrete models, the set where the reactant vanishes plays an important role and is known as the dead core. Because boundary of dead core is unknown a priori, this is a free boundary problem. Firstly, using the maximun principle and the comparison principle, lower bound and upper bound for boundary values are derived by dint of solutions of corresponding Dirichlet problem, it shows the existence of the dead core. Then some estimates for the location and shape of the dead core on general domain are obtained. These results are improvement and extension of existing results.