Mathematical Sciences: Some Questions in Nonlinear Differential Equations

数学科学：非线性微分方程的一些问题

• 批准号: 9500570
• 负责人: Paul Rabinowitz
• 金额: $ 20.27万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-05-15 至 1999-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9500570&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Some; Questions; Nonlinear

PI: Rabinowitz DMS-9500570 Rabinowitz will investigate the existence of basic homoclinic solutions of Hamiltonian systems of various types such as singular systems, systems where there seem to be solutions homoclinic to infinity, and systems with almost periodic potentials. Once basic homoclinics have been determined, recent variational methods suggest that one can also find infinitely many so-called multibump solutions which are near sums of translates of the basic solutions. This is another question Rabinowitz will pursue. Finally, for PDE's he will look at some nonlinear wave and Schrodinger equations with almost periodic potentials. Partial differential equations form a basis for mathematical modeling of the physical world. The role of mathematical analysis is not so much to create the equations as it is to provide qualitative and quantitative information about the solutions. This may include answers to questions about uniqueness, smoothness and growth. In addition, analysis often develops methods for approximation of solutions and estimates on the accuracy of these approximations.

PI：Rabinowitz DMS-9500570 拉比诺维茨将调查存在的基本同宿解的哈密顿系统的各种类型，如奇异系统，系统似乎有解决方案同宿无穷大，系统与几乎周期的潜力。 一旦基本同宿已经确定，最近的变分方法表明，人们也可以找到无限多个所谓的多凸解，这些多凸解是基本解的平移的近和。 这是拉宾诺维茨要探讨的另一个问题。 最后，对于偏微分方程的，他将着眼于一些非线性波和薛定谔方程几乎周期的潜力。 偏微分方程是物理世界数学建模的基础。 数学分析的作用与其说是建立方程，不如说是提供关于解的定性和定量信息。 这可能包括关于独特性，平滑性和增长的问题的答案。 此外，分析经常发展出解的近似方法和对这些近似的准确性的估计。