一类空间非均匀环境下含时滞的反应扩散方程的自由边界问题  

A FREE BOUNDARIES PROBLEM FOR REACTION-DIFFUSION EQUATIONS WITH TIME DELAY IN HETEROGENEOUS ENVIRONMENTS

作　　者：唐静 陈玉娟[1] 王晓燕[1] Tang Jing;Chen Yujuan;Wang Xiaoyan(School of Sciences,Nantong University,Nantong 226019)

机构地区：[1]南通大学理学院,南通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。

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.

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 

分 类 号：O175.26[理学—数学]