有孔区域上一类具非局部边值条件的非线性扩散方程

A Class of Nonlinear Diffusion Equations with Nonlocal Boundary Value Condition in Perforated Domains

利用打靶法、上下解方法和不动点定理等工具,研究有孔区域上一类具非局部边值条件的非线性扩散方程.分别在径向稳态情形、非径向稳态情形及非稳态情形下,得到了方程解的存在性以及孔点的性质.

The shooting method, sub and super solution method, and fixed point theorem were used to study a class of nonlinear diffusion equations with nonlocal boundary value condition in perforated domains. We discussed the existence of the solutions and the removability of the orifice at the radial steady states, non-radial steady states and non-steady states.