Spatio-temporal dynamics of general diffusive processes in heterogeneous and random environments

异构随机环境中一般扩散过程的时空动力学

• 批准号: RGPIN-2018-04371
• 负责人: Shen, Zhongwei
• 金额: $ 1.53万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=665005
• 关键词: Spatio; temporal; dynamics; general; diffusive

General diffusive processes, such as the spread of advantageous genes, the invasion of species, the migration of forest types, the propagation of flames, and the spread of infectious diseases, include both classical diffusive processes and nonlocal dispersal processes, and arise in many scientific areas such as chemistry, chemical engineering, combustion theory, ecology, epidemiology and population biology. Evolutionary equations have been widely used to model and study the evolution of general diffusive processes. Classical studies of evolutionary equations assume the environment is homogeneous in both space and time. However, many general diffusive processes in the real world encounter spatial and temporal fluctuations due to the change of environmental conditions, and such fluctuations have great influences on the persistence and spread of these processes. This motivates the study of evolutionary equations in heterogeneous and random environments. ******The primary goal of the proposed research program is to investigate spatio-temporal dynamics of evolutionary equations in heterogeneous and random environments. The main objectives include:******1. the investigation of the persistence theory, the global dynamics, the spreading properties of propagating solutions, and the existence, stability and qualitative properties of generalized travelling fronts for several important classes of evolutionary equations in heterogeneous or random environments, including reaction-diffusion equations in heterogeneous environments, stepping stone models or stochastic Fisher-Kolmogorov-Petrowsky-Piscunov equations, and integrodifference equations with random coefficients;******2. the study of population persistence under climate change by investigating a class of integrodifference equations subject to climate change described by the location, the velocity and the geometry of a finite favourable habitat, that moves inside the surrounding unfavourable environment.******The proposed research program is expected to advance and enrich the theory of evolutionary equations in heterogeneous and random environments, to introduce new mathematical ideas and methods to study evolutionary equations for more realistic models, and to provide mathematical frameworks and tools for applications in many areas of science and engineering.

一般的扩散过程，例如有利基因的传播，物种的侵袭，森林类型的迁移，火焰的传播以及传染性疾病的传播，包括经典的扩散过程和非局部分散过程，以及在许多科学领域，例如化学工程，化学工程学，燃烧理论，生物学，植物学和人群学和种群。进化方程已被广泛用于建模和研究一般扩散过程的演变。进化方程的经典研究假定环境在时空和时间上都是均匀的。但是，由于环境条件的变化，许多现实世界中的许多一般扩散过程遇到了空间和时间波动，并且这种波动对这些过程的持久性和传播产生了很大的影响。这激发了对异质和随机环境中进化方程的研究。 *****拟议的研究计划的主要目标是研究异质和随机环境中进化方程的时空动力学。主要目标包括：****** 1。 the investigation of the persistence theory, the global dynamics, the spreading properties of propagating solutions, and the existence, stability and qualitative properties of generalized travelling fronts for several important classes of evolutionary equations in heterogeneous or random environments, including reaction-diffusion equations in heterogeneous environments, stepping stone models or stochastic Fisher-Kolmogorov-Petrowsky-Piscunov equations, and integrodifference具有随机系数的方程； ****** 2。通过调查由位置所描述的气候变化，速度和几何形式所描述的有限良好栖息地的几何形式所描述的一系列综合差异方程来研究气候变化下的人口持久性的研究。******************更现实的模型，并为许多科学和工程领域的应用提供数学框架和工具。