摘要
本文首先讨论了一类空间非均匀环境下含时滞的反应扩散方程ut=duxx+f(t,x,u(t,x),u(t-τ,x))的自由边界问题,其解的局部存在性、唯一性及古典解的全局存在性也已证得.特别地,对于方程ut=duxx+f(u(t,x),u(t-τ,x))的自由边界问题,我们研究了解的长时间行为并给出了传播—消失二择一结果.
This paper is concerned with a free boundaries problem for the reactiondiffusion equation ut=duxx+f(t,x,u(t,x),u(t-τ,x))with time delay in heterogeneous environments.Local existence and uniqueness and further global existence of a classical solution are obtained.Then for the special equation ut=duaa+f(u(t,a),u(t-T,a))with free boundaries,we give the long-time behavior of the solutions and establish a vanishing-spreading dichotomy result.
作者
唐静
陈玉娟
王晓燕
Tang Jing;Chen Yujuan;Wang Xiaoyan(School of Sciences,Nantong University,Nantong 226019)
出处
《南京大学学报(数学半年刊)》
2022年第2期121-145,共25页
Journal of Nanjing University(Mathematical Biquarterly)
基金
Supported by NSFC Grant 12171258。
关键词
存在性与唯一性
自由边界
时滞
非均匀环境
传播—消失二择一
Existence and uniqueness
free boundaries
time delay
heterogeneous environments
vanishing-spreading dichotomy.