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: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635634
• 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 theinteraction between them. Main research topics in future five years include the study of traveling waves and speed selection, pattern formation(spike, shock and spotpatterns) 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 forreaction diffusion models. The recent progresstowards the combined effect of spatial diffusion and temporalevolution leads to some interesting reaction diffusion equations. These models have been extensively studied in physical, biological and chemicalsciences. The qualitative andquantitative analysis of nonlinear dynamics (e.g. travelingwavefronts, stability of their steady state in a bounded domain)of these popular systems are the main purposeof 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 patternsmodeled by reaction diffusion equations on surfaces. Thecharacterization of pattern formations and exponentially slow internal layer motion(metastable-motion) in various physical, biological and chemicalmodels will be another subject of my future research. My goal isto give qualitative and quantitative analysis of formation and movement of spot layer solutions that exhibit inreaction-diffusion systems on surfaces.3) Analysis and approximation of solutions to singularly perturbedpartial differential equations on surfaces. I will study the approximation of solutions to boundary value problems for singularly perturbedpartial 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.

该方案的研究是应用动力系统和渐近分析两个领域的结合，以及它们之间的相互作用。未来五年的主要研究课题包括行波与速度选择研究、表面斑图形成（尖峰、激波和斑图）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）反应扩散模型的波传播模式和波速选择机制分析。 近年来，由于空间扩散和时间演化的综合作用，产生了一些有趣的反应扩散方程。这些模型在物理、生物和化学等领域得到了广泛的研究。对这些流行系统的非线性动力学（如行波波前、定态在有界区域内的稳定性）进行定性和定量分析是我今后研究的主要目的。特别是，我们感兴趣的行波图案的存在性和波速选择机制。2）分析图案的形成和亚稳态运动的斑点图案由表面上的反应扩散方程模型。在各种物理、生物和化学模型中，图案形成和指数慢内层运动（亚稳态运动）的特征将是我未来研究的另一个主题。我的目标是定性和定量地分析表面上反应扩散系统的点层解的形成和运动。3）表面上奇摄动偏微分方程的解的分析和逼近。 我将研究曲面上奇摄动偏微分方程边值问题解的逼近。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。