兰州大学机构库 >数学与统计学院
周期介质中反应对流扩散方程脉动行波解的渐近行为和整体解
Alternative TitleAsymptotic Behavior of Pulsating Fronts and Entire Solutions for Reaction Advection Diffusion Equations
步真会
Thesis Advisor王智诚
2014-05-22
Degree Grantor兰州大学
Place of Conferral兰州
Degree Name硕士
Keyword反应对流扩散方程 周期介质 脉动行波解 渐近行为 整体解
Abstract在生态学和生物学等学科的研究中, 所有的生物种群都是在一定的空间区域中生活的, 而生物种群生活的外部环境如食物、湿度、温度等资源都是随着地点和时间的变化而发生周期性的改变. 在物理、工程、化学等方面, 也存在着周期 性变化的介质环境. 因此, 这就需要我们在周期的介质中研究反应-对流-扩散方 程. 本文主要研究周期介质中反应-对流-扩散方程的脉动型行波解的指数衰减行 为和整体解. 首先, 叙述了本文的研究背景、研究进程和研究的问题. 其次, 当方程的非线性项为双稳型时, 研究了方程的脉动型行波解的渐近行 为. 利用比较原理, 我们得到当s → ±∞ 时, 方程的脉动型行波解是指数衰减的. 最后, 研究了上述方程的整体解. 我们假设方程具有三个平衡点, 其中一个 是线性化不稳定的, 两个是线性化稳定的, 任意两个平衡点之间都存在脉动型行 波解. 我们首先利用脉动型行波解的指数衰减行为得到了一些先验估计, 然后构 造合适的上下解, 再利用比较原理和上下解方法得到了两种类型的脉动型整体解 并给出了他们的定性性质.
Other AbstractIn the study of ecology, biology, and so on, all biotic populations live in some space region, where the external environment including food, humidity and temperature changes with the location and time periodically. The periodic variation of media also happens in the fields of physics, engineering and chemistry. Therefore, it is of great significance to study the reaction-advection-diffusion equations in periodic media. In this paper, we study the asymptotic behavior of pulsating fronts and entire solutions of reaction-advection-diffusion equations in periodic media. Firstly , we mainly discuss the research background and give a brief introduction to the problem of this article. Secondly, we study the asymptotic behavior of pulsating fronts of reactionadvection- diffusion equations with bistable nonlinearity in periodic media. By using comparison principle and the method of super-subsolutions, we obtain that the pulsating fronts is exponential decay as s → ±∞. Lastly, we study the entire solutions of the above equation. Assume that the equation admits three equilibria: one is linearly unstable and the others are linearly stable and that there are different pulsating fronts connecting any two of them. Utilizing the previous conclusion that pulsating fronts decay exponentially, we get some prior estimates. Then we construct suitable sub-super solutions. After that, we establish two different types of pulsating entire solutions and obtain the qualitative properties of them by combing comparison principle with subsuper solution method.
URL查看原文
Language中文
Document Type学位论文
Identifierhttps://ir.lzu.edu.cn/handle/262010/224343
Collection数学与统计学院
Recommended Citation
GB/T 7714
步真会. 周期介质中反应对流扩散方程脉动行波解的渐近行为和整体解[D]. 兰州. 兰州大学,2014.
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