关于稳态反应扩散对流方程的死核问题

本文研究带参数λ的稳态反应扩散对流方程△u=λf(u,Du)的死核问题,证明了当函数f满足一定的条件时,对每个有界光滑区域Ω存在相应的正数λ(Ω)使当λ>λ(Ω)时该方程在边值条件u=1下的非负解有死核,并讨论了死核随λ的变化情况。

On the Dead Core Problem for Steady-State Reaction-Diffusion-Convection Equations

This paper studies the dead core problem for the steady-state reaction-diffusion-convection equation u= f(u,Du) ,where Ais a positive parameter. It is proved that under certain conditions on the nonlinear term f ,for every bounded smooth domain Rn there is a corresponding positive number such that the solution u of this equation on under the boundary condition u |= 1 has dead core when . The problem of how the dead core varies as A approaches to is also studied.