一个具有非局部效应的非线性周期反应扩散方程的渐近形态

黄业辉, 翁佩萱

数学学报 ›› 2014, Vol. 57 ›› Issue (5) : 1011-1030.

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数学学报 ›› 2014, Vol. 57 ›› Issue (5) : 1011-1030. DOI: 10.12386/A2014sxxb0094
论文

一个具有非局部效应的非线性周期反应扩散方程的渐近形态

    黄业辉1,2, 翁佩萱2
作者信息 +

Asymptotic Patterns for a Nonlinear Periodic Reaction-Diffusion Equation with Nonlocal Effect

    Ye Hui HUANG1,2, Pei Xuan WENG2
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文章历史 +

摘要

研究一个具有非线性-非局部反应的周期反应扩散系统.利用周期半流的渐近理论来讨论渐近波速c*和周期行波解的存在性,证明参数c*也是周期行波解的最小波速,并 清晰描述解传播的阈值性质.最后给出渐近波速和最小波速c*的估计.

Abstract

A periodic reaction-diffusion system with nonlinear-nonlocal functional response is considered in this paper. We use the asymptotic theory for periodic semiflow to discuss the existence of spreading speed c* and periodic traveling wave solutions. The threshold property for the spreading spread of solutions is described clearly according to the threshold parameter c* which is exactly the minimal wave speed as well. Finally, we give an estimate of the spreading speed and minimal wave speed c*.

关键词

渐近波速 / 周期行波解 / 非局部效应

Key words

spreading speed / periodic traveling wave solution / nonlocal effect

引用本文

导出引用
黄业辉, 翁佩萱. 一个具有非局部效应的非线性周期反应扩散方程的渐近形态. 数学学报, 2014, 57(5): 1011-1030 https://doi.org/10.12386/A2014sxxb0094
Ye Hui HUANG, Pei Xuan WENG. Asymptotic Patterns for a Nonlinear Periodic Reaction-Diffusion Equation with Nonlocal Effect. Acta Mathematica Sinica, Chinese Series, 2014, 57(5): 1011-1030 https://doi.org/10.12386/A2014sxxb0094

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基金

国家自然科学基金(11171120);教育部高等学校博士学科点专项科研基金(20094407110001);广东省自然科学基金项目(10151063101000003)

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