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U.S.-Polish Cooperative Research: Lyapunov Exponents and Spectrum for Random and Nonautonomous Parabolic Equations

美波合作研究：随机和非自治抛物型方程的李亚普诺夫指数和谱

基本信息

批准号：
0341754
负责人：
Wenxian Shen
金额：
$ 1.06万
依托单位：
Auburn University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2004
资助国家：
美国
起止时间：
2004-06-01 至 2007-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=0341754&HistoricalAwards=false
关键词：
U.S.Polish Cooperative Research Lyapunov

项目摘要

This is a U.S.-Polish cooperative research project that focuses on the links between the spectrum of a given parabolic system and its Lyapunov exponent. The principal investigators are Dr. Wenxian Shen from Auburn University and Professor Janusz Mierczynski from Wroclaw University of Technology. The objective of the proposed research is to investigate spectrum/Lyapunov exponents for nonautonomous/random parabolic equations and to study their applications. In nature, many systems are subject to time dependence. Such dependence may be neither periodic nor quasi-periodic or almost periodic. Systems with such time dependence are characterized more appropriately by nonautonomous or random equations. It is therefore of great importance to study general nonautonomous and random equations. The proposed research focuses on the development of linear theory, namely spectrum/Lyapunov exponents theory, for nonautonomous/random parabolic equations. Such theory would have important applications to nonlinear equations. The most obvious of these is its role played in the analysis of the stability of certain special solutions of nonlinear parabolic equations. This project in mathematics research fulfills the program objectives of bringing together leading experts in the U.S. and Central/Eastern Europe to combine complementary efforts and capabilities in areas of strong mutual interest and competence on the basis of equality, reciprocity, and mutuality of benefit.

这是一个美国-波兰合作研究项目，重点研究特定抛物系统的频谱与其李雅普诺夫指数之间的联系。主要研究者是奥本大学的沈文贤博士和弗罗茨瓦夫理工大学的Janusz Mierczynski教授。研究非自治随机抛物方程的谱/Lyapunov指数及其应用。在自然界中，许多系统都具有时间依赖性。这种依赖性既不是周期性的，也不是准周期性的或几乎周期性的。具有这种时间依赖性的系统更适合用非自治或随机方程来描述。因此，研究一般非自治随机方程具有重要意义。拟议的研究重点发展的线性理论，即谱/李雅普诺夫指数理论，非自治/随机抛物型方程。这样的理论对非线性方程有重要的应用。其中最明显的是它在分析非线性抛物方程某些特解的稳定性中所起的作用。这个数学研究项目实现了汇集美国和中欧/东欧领先专家的计划目标，在平等，互惠和互利的基础上，在强烈的共同利益和能力领域联合收割机互补努力和能力。