U.S.-Japan Cooperative Research: Topological and Singular Perturbation Methods with Applications to Nonlinear Differential Equations

9315117本奖项支持佐治亚理工学院动力系统和非线性研究中心的Konstantin Mischaikow教授和日本广岛大学数学系的西浦康萨教授之间为期两年的合作研究项目。该项目的目标是通过将分析方法和拓扑方法相结合来开发用于动力系统的理论技术，然后将它们应用于由反应扩散方程组引起的几个问题。另外两名日本研究人员--京都大学的Hiroshi Kokubu和琉球大学的Hiroe Oka--也将参与该项目。在访问日本期间，Mischaikow教授将尝试结合动力学和分叉理论的两种观点：主要基于他的专长Conley指数的代数拓扑学方法和以三名日本研究人员为代表的基于奇异摄动理论的分析方法。该项目的长期目标是利用这些信息来了解由偏微分方程产生的特定动力系统中复杂的、可能是混沌的动力学现象。一些原型模型、新方法和初步结果已经通过美国和日本研究小组的事先合作取得了。***

9315117 Mischaikow This awards supports a two-year cooperative research project between Professor Konstantin Mischaikow, Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology, and Professor Yasumasa Nishiura, Department of Mathematics, Hiroshima University, Hiroshima, Japan. The objective of the project is to develop theoretical techniques for use in dynamical systems by integrating analytical and topological methods, and then to apply them to several problems arising from systems of reaction diffusion equations. Two other Japanese researchers -- Hiroshi Kokubu of Kyoto University and Hiroe Oka of Ryukoku University -- will also participate in the project. During his visits to Japan, Professor Mischaikow will attempt to combine two viewpoints of dynamics and bifurcation theory: an algebraic-topologic approach, based primarily on the Conley index, which is his expertise, and an analytic approach based on singular perturbation theory represented by the three Japanese researchers. The long-range goal of the project is to use the information to understand the appearance of complicated, possibly chaotic, dynamics in specified dynamical systems generated by partial differential equations. Some prototype models, new approaches, and preliminary results have already been achieved through prior collaboration of the U.S. and Japanese research groups. ***