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: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=709435
• 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.

这项建议中的研究结合了两个领域： 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课题包括行波与速度选择、图形形成(尖峰、激波和斑点)的研究 曲面和渐近分析(例如，奇异摄动和边界层理论)。本文的研究范围和目标是：1)波传播模式分析和波速选择机制 反应扩散模型。最近的进展 论空间扩散和时间效应的综合作用 进化导致了一些有趣的反应扩散方程。这些模型已经在物理、生物和化学方面进行了广泛的研究。 科学。质的和 非线性动力学的定量分析(例如旅行 波前，其稳态在有界域中的稳定性) 这些流行的系统中的主要目的是 在我未来的研究中。特别是，我们对行波模式的存在和波速选择机制感兴趣。 2)斑点花样的形成和亚稳态运动分析 由表面上的反应扩散方程建模。这个 花样形成和指数慢的内层运动的特征 (亚稳态运动)在各种物理、生物和化学中 模特将是我未来研究的另一个主题。我的目标是 以定性和定量地分析Spot Layer溶液的形成和运动 表面上的反应扩散系统。 3)奇摄动解的分析与逼近 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。给出了近似解的误差界，为以往文献中的一些形式分析提供了严格的论证。 从理论上讲，这一建议证明了应用动力系统理论和渐近分析的新发展。这项研究在生物、物理等其他科学领域的应用中也具有重要意义。通过这项建议，旨在建立我校一流的研究团队，这也是对加拿大数学学会的重大贡献。