项目名称: 具有非单调结构反应扩散方程组的分歧解研究
项目编号: No.11201101
项目类型: 青年科学基金项目
立项/批准年度: 2013
项目学科: 数理科学和化学
项目作者: 王金凤
作者单位: 哈尔滨师范大学
项目金额: 22万元
中文摘要: 本项目以带参数反应扩散方程组分歧解集的研究为核心,拟结合偏微分方程和无穷维动力系统方法,建立具有非单调结构反应扩散方程组的全局分歧解图,扩大刻划非单调系统的模式生成理论;在此基础上,建立一个较为系统完全的非单调反应扩散方程组定性分析的基本框架,进而为更精确地描述其全局时空动力学行为提供新的方法和途径。 与单个方程和具有单调结构的方程组相比,具有非单调结构的反应扩散方程组没有最大值原理,导致强有力的比较方法失效,从而给全局解的研究带来很大的困难。本项目的顺利进行不仅发展和丰富了具有单调结构反应扩散方程组已有的工具,而且能够补充新的方法和技巧。
中文关键词: 反应扩散;非单调;周期解;静止状态;分歧
英文摘要: The proposal focus on the bifurcation solutions for reaction diffusion systems with non-monotone structure. Using the tooles from partial differential equations and infinite dimensional dynamical systems, our main effort is to establish the global bifurcation diagrams of reaction diffusion systems with non-monotone structure, and to enlarge the theory of pattern formation for non-monotone systems. Based on this, we hope to develop a more general framework for the qualitative analysis of reaction diffusion systems and provide a new approach to describe their globally spatiotemporal dynamical behavior more precisely. Compared with the scalar equation or systems with monotone structure, systems with non-monotone structure have no maximum principle,which leads to the failure of powerful comparison methods. Therefore, it is more difficult to study the global solutions to systems with non-monotone. It not only develops and improves the available tools for monotone systems, but also supplements some new approach and technique if the proposal were carried out smoothly.
英文关键词: reaction-diffusion;nonmonotonic;periodic solution;quiescence state;bifurcation