Applied dynamical systems and asymptotic analysis

应用动力系统和渐近分析

• 批准号: RGPIN-2016-04709
• 负责人: Ou, Chunhua
• 金额: $ 1.31万
• 依托单位: Memorial University of Newfoundland
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=615255
• 关键词: Applied; dynamical; systems; asymptotic; analysis

The research in this proposal is a combination of two fields: applied dynamical systems and asymptotic analysis, as well as the interaction between them. Main research topics in future five years include the study of traveling waves and speed selection, pattern formation(spike, shock and spot patterns) on surfaces and asymptotic analysis (e.g., singular perturbation and boundary layer theory). The research scope and objectives are: 1) Analysis of wave-propagation patterns and wave-speed selection mechanics for reaction diffusion models. The recent progress towards the combined effect of spatial diffusion and temporal evolution leads to some interesting reaction diffusion equations. These models have been extensively studied in physical, biological and chemical sciences. The qualitative and quantitative analysis of nonlinear dynamics (e.g. traveling wavefronts, stability of their steady state in a bounded domain) of these popular systems are the main purpose of my research in the future. In particular, we are interested in the existence of traveling wave-patterns and the wave-speed selection mechanics. 2) Analysis of pattern formations and metastable-motion of spot patterns modeled by reaction diffusion equations on surfaces. The characterization of pattern formations and exponentially slow internal layer motion (metastable-motion) in various physical, biological and chemical models will be another subject of my future research. My goal is to give qualitative and quantitative analysis of formation and movement of spot layer solutions that exhibit in reaction-diffusion systems on surfaces. 3) Analysis and approximation of solutions to singularly perturbed partial differential equations on surfaces. I will study the approximation of solutions to boundary value problems for singularly perturbed partial differential equations on surfaces. Error bounds of the approximate solutions will be provided and this will give rigorous arguments to some formal analysis in past references. Theoretically, this proposal demonstrates the establishment of new developments in the theory of applied dynamical systems and asymptotic analysis. The research is also important in the applications to other sciences such as biology and physics. Through the proposal, it is intended to establish a first-class research team in our university and this also contributes greatly to the Canadian mathematical society.

本提案中的研究是两个领域的结合： 应用动力系统和渐近分析，以及 他们之间的互动。未来五年的主要研究方向包括行波与速度选择、波型形成（棘波、冲击波和斑点波）的研究 图案）和渐近分析（例如，奇异摄动和边界层理论）。本文的研究内容和目标是：1）分析了波浪在水下的传播模式和波速选择机理， 反应扩散模型的最新进展 空间扩散和时间的综合效应 演化导致了一些有趣的反应扩散方程。这些模型已经在物理、生物和化学方面得到了广泛的研究 以理工科为重定性和 非线性动力学的定量分析（例如， 波前，在有界区域内稳定状态的稳定性） 这些流行的系统的主要目的是 我的研究在未来。特别是，我们感兴趣的行波模式的存在和波速选择机制。 2)斑图的形成与亚稳态运动分析 由表面上的反应扩散方程建模。的 图案形成和指数缓慢内层运动的表征 （亚稳态运动）在各种物理，生物和化学 模型将是我未来研究的另一个主题。我的目标是 定性和定量分析了斑点层溶液的形成和运动， 表面上的反应扩散系统 3)奇摄动方程解的分析与逼近 曲面上的偏微分方程我将研究奇摄动边值问题解的逼近 曲面上的偏微分方程将提供近似解的误差界，这将给严格的参数，在过去的参考文献中的一些形式化的分析。 从理论上讲，这一建议表明了应用动力系统和渐近分析理论的新发展。这项研究在生物学和物理学等其他科学的应用中也很重要。通过该提案，旨在建立一流的研究团队，在我们的大学，这也大大有助于加拿大数学社会。