Hamiltonian Partial Differential Equations

哈密​​顿偏微分方程

• 批准号: 250233-2012
• 负责人: Colliander, James
• 金额: $ 3.79万
• 依托单位: University of British Columbia
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2015
• 资助国家: 加拿大
• 起止时间: 2015-01-01 至 2016-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=570856
• 关键词: Hamiltonian; Partial; Differential; Equations

Continuum vibrations in physical settings, like the motions of a lake's surface, light waves in a fiber optic channel or spacetime metric oscillations caused by the ringdown of a binary star system are mathematically modeled by equations like the Euler and Maxwell systems, the nonlinear Schrödinger and Einstein equations. Even though they arise in descriptions of wildly diverse physical phenomena, the equations that model continuum vibrations without friction enjoy rich mathematical similarities (e.g. conserved quantities like energy and mass, Hamiltonian formulation, symplectic phase space, ...) which define the conceptual framework for the field of Hamiltonian partial differential equations. The goal of the proposed research is to contribute to the general understanding of the maximal-in-time behavior of solutions of the initial value problem for Hamiltonian PDE. The aim is to produce new answers to the main question about evolution equations: what happens?

物理环境中的连续振动，如湖面的运动，光纤中的光波 由二元星星系统的衰荡引起的通道或时空度规振荡由类似于欧拉和麦克斯韦系统、非线性薛定谔和爱因斯坦方程的方程数学建模。尽管它们出现在各种各样的物理现象的描述中，但模拟无摩擦连续振动的方程具有丰富的数学相似性（例如能量和质量等守恒量，哈密顿公式，辛相空间等）。它定义了哈密顿偏微分方程领域的概念框架。所提出的研究的目标是有助于一般的理解的最大的时间行为的解决方案的初始值问题的哈密顿偏微分方程。其目的是为进化方程的主要问题：发生了什么？