Mathematical Scienecs: Linear and Nonlinear Waves

数学科学：线性波和非线性波

• 批准号: 9401777
• 负责人: Avraham Soffer
• 金额: $ 5.6万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-15 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9401777&HistoricalAwards=false
• 关键词: Mathematical; Scienecs; Linear; Nonlinear; Waves

9401777 Soffer Two main topics will be investigated. In the Cauchy problem for the nonlinear wave equation, the results of Ginibre-Soffer- Velo on the critical power nonlinear wave equation which are complete for the radial case will be further developed to include the general data. It is based on applying new Lebesgue pth power bounds which allow the control of the p-norm of a function in terms of singular weighted norms and partial regularity. In the theory of three body dispersive systems a new class of dilations, deformed by various partitions of unity to cluster decompositions will be used. This will allow proofs of local decay and other spectral properties of three body dispersive equations. Modern physics, quantum mechanics and relativity, is a product of the twentieth century. It is founded firmly in the last century's attempt to address the microstructure of matter and to come to grips with the concept of action-at-a distance, electro-magnetism, and heat radiation. The mathematical foundations for these developments collectively called mathematical physics, ranges from detailed analysis of Schroedinger operators, which governs the dynamics of particles, to unified field theory, which attempts to unite the four known forces into a single force. ***

9401777将研究两个主要主题。在非线性波方程的Cauchy问题中，将进一步开发用于径向案例的临界功率非线性波方程的Ginibre-Soffer-velo的结果，以包括一般数据。它基于应用新的Lebesgue PTH功率界限，该界限允许根据奇异加权规范和部分规律性控制功能的p-norm。在三个身体分散系统的理论中，将使用各种统一分配到群集分解的新扩张。这将允许证明三个身体色散方程的局部衰减和其他光谱特性。 现代物理学，量子力学和相对论是20世纪的产物。它是在上个世纪旨在解决物质微观结构并掌握动作距离，距离，电磁性和热辐射的概念的尝试中牢固建立的。这些发展的数学基础共同称为数学物理学，范围从控制粒子动力学的施罗丁格运营商的详细分析到统一的田间理论，这些田间理论试图将四个已知的力团结成单力。 ***