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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
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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)
机构地区 南通大学理学院
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.
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