南通大学学报（自然科学版）2018，Vol.17Issue(3)：66-70,5.
一类半线性反应扩散方程组自由边界问题的爆破性
The Blow-Up Properties of a Semi-linear Reaction-Diffusion Problem with Free Boundary
摘要
Abstract
In this paper, the free boundary model of a class of semi-linear reaction diffusion equations is presented.Firstly, the relationship between the positive solutions of the model when the blow-up case occurs is analyzed, and the results of simultaneous blow-up are obtained by rescaling the independent variables. Secondly, it is proved that the solution of the model is monotonically decreasing in some regions, by constructing auxiliary functions and using internal Schauder estimation. Finally, by using the contradiction method, the result that the blow-up set is the compact subset of the initial area is obtained by constructing the auxiliary function and using the maximum principle, while in this case, the free boundary is bounded.关键词
反应扩散方程/自由边界/爆破/爆破集Key words
reaction-diffusion equation/free boundary/blow up/blow-up sets分类
数理科学引用本文复制引用
俞静秋,陆海华..一类半线性反应扩散方程组自由边界问题的爆破性[J].南通大学学报（自然科学版）,2018,17(3):66-70,5.基金项目
国家自然科学基金项目 (11501309) （11501309）
江苏省"青蓝工程"优秀青年骨干教师项目 （）
