非局部扩散单稳方程传播速度的线性和非线性选择 Alternative Title Linear and nonlinear selections of spreading speed for nonlocal dispersal equations with momostable nonlinearity 张海玲 Subtype 硕士 Thesis Advisor 李万同 2021-06-17 Degree Grantor 兰州大学 Place of Conferral 兰州 Degree Name 理学硕士 Degree Discipline 应用数学 Keyword 非局部扩散 行波解 比较原理 单调动力系统 渐近传播速度 Abstract 本文研究了非局部扩散单稳方程的传播速度问题.当非线性在零点处非退化时,利用已有的抽象理论并借助上下解方法及比较原理,给出了传播速度线性和非线性选择的充分条件,进一步刻画了非局部扩散Fisher-KPP方程的最小传播速度是通过其线性速度定义的合理性,同时在这种情形下,给出了带有离散时滞的非局部扩散方程的速度选择机制.当非线性退化时,由于线性速度为零以及临界波速的正性,通过解的长时间行为的特殊性,给出了行波解满足特定衰减行为时对应的波速即为临界波速*,从而克服了临界波速无法被线性决定的事实,给出了传播速度被非线性选择的条件,并且借助充分小的正数,具体的描述了退化情形下的传播速度,在不同的角度上给出了临界波速的刻画. Other Abstract In this paper, we consider that the question of spreading speed for nonlocaldispersal equations with monostable nonlinearity. we consider that the sufficientcondition for the nonlinear and linear selections of the spreading speed establishedby comparison principle and upper and lower solutions which is based on abstractmethod when the nonlinear term is nondegenerate at zero point, we give a furtherdepiction of rationality which minimal speed is defined by linear speed when nonlocal dispersal equations with Fisher-kpp nonlinearity, meanwhile, in this situation, wegive the mechanism of speed selection which the equation has discrete delay. whenwe consider that nonlinear term is degenerate, because of the linear speed is zero,and critical speed is nonnegative, hence the critical speed can not be determined bythe linear speed, however we can give a depiction of critical speed through speciallong-time behavior of traveling wave solution, at the same time, we get the nonlinearselection conditions, and we specifically describe spreading speed for nonlocal dispersal equation with degenerate nonlinearity through, which is sufficiently small,thus we give a certain characterization in different angles. Pages 51 URL 查看原文 Language 中文 Document Type 学位论文 Identifier https://ir.lzu.edu.cn/handle/262010/462310 Collection 数学与统计学院 Affiliation 数学与统计学院 First Author Affilication School of Mathematics and Statistics Recommended CitationGB/T 7714 张海玲. 非局部扩散单稳方程传播速度的线性和非线性选择[D]. 兰州. 兰州大学,2021.
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