空间周期时滞非局部反应扩散方程的动力学研究

项目名称： 空间周期时滞非局部反应扩散方程的动力学研究

项目编号： No.11301407

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 吴事良

作者单位： 西安电子科技大学

项目金额： 23万元

中文摘要： 时滞非局部反应扩散方程的研究正处于迅速发展的阶段。现有的模型大多考虑的是均衡环境的情形，而实际问题常常需要考虑环境的非均衡性特别是周期性对系统动力学行为的影响。本项目拟研究空间周期环境下时滞非局部反应扩散方程的动力学行为，主要内容包括：研究空间周期时滞非局部反应扩散方程中波的传播现象，发展(脉动)行波解问题的一般理论方法；研究空间周期时滞非局部反应扩散方程的行波解之间的交互作用及相关的整体解问题，建立整体解的抽象结果并发展相关方法；特别地，研究空间周期性、时滞及非局部效应等因素对系统动力学行为的影响，分析这些结果与空间周期时滞格微分方程动力学行为之间的本质差异。本项目源自于生物学、传染病学等领域的许多实际问题，具有重要的理论意义和应用价值。项目的完成将为周期环境下反应扩散方程的动力学研究提供一些新的研究思路和方法，进一步丰富反应扩散方程理论。

中文关键词： 反应扩散方程；空间周期环境；时滞和非局部效应；行波解；整体解

英文摘要： In the recent years, quite a few studies have been devoted to delayed nonlocal reaction-diffusion equations with homogeneous environment. However, the real environments are generally heterogeneous due to natural phenomena or exposure to artificial distributions. It is very important to understand how heterogeneities influence the ecological dynamics. Clearly, a simple form of heterogeneous environment is the periodic habitat. In this project, we will study the dynamics of delayed nonlocal reaction-diffusion equations in spatially periodic habitats. Our main concerns are the existence, asymptotic behavior, uniqueness and stability of pulstating traveling front solutions and entire solutions. Moreover, we will study the dependence of the minimal wave speed on the spatial periodicity, delay and nonlocal effect. In particular, we will consider the essential differences of the dynamics between the spatially discrete and continuous delayed nonlocal reaction-diffusion equations in spatially periodic habitats. This project arises from many practical problems in some applied fields, such as biology, epidemiology and so on. It has a very important theoretical significance and application value. A definite breakthrough in the theory and methods may be made and contribute to the further development of the theory of reaction

英文关键词： reaction-diffusion equation；spatially periodic habitat；delay and nonlocal effect；traveling wave solution；entire solution