Systems of Nonlinear Partial Differential Equations in Transport Theory

输运理论中的非线性偏微分方程组

基本信息

批准号：
9321383
负责人：
Robert Glassey
金额：
$ 12.08万
依托单位：
Indiana University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
1994
资助国家：
美国
起止时间：
1994-07-01 至 1999-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9321383&HistoricalAwards=false
关键词：
Systems Nonlinear Partial Differential Equations

项目摘要

9321383 Glassey This award supports research on systems of nonlinear partial differential equations and applications to plasma theory. The work involves both analytical and numerical points of view. The emphasis is on collisional effects in problems arising in plasma physics. This involves the modification of the Vlasov- Maxwell systems through the addition of collision operators of Boltzmann- and Landau-type. The major thrust of this effort is dedicated to the study of Landau damping, in which the long time behavior the initial value problem for the linearized Vlasov equation is prescribed. Work has already been done on finding optimal decay rates in the relativistic case, in which the range of validity is restricted by the fact that collisional effects are neglected. Emphasis will now be placed on understanding decay in the nonrelativistic setting. Studies will also be made on the Vlasov-Einstein system to include a fully relativistic model for stellar dynamic problems. The work is important because of its relation to cosmic censorship. 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. ***

9321383 Glassey该奖项支持有关非线性偏微分方程系统以及血浆理论应用的研究。这项工作涉及分析和数值的观点。重点是在血浆物理学中引起的问题中的碰撞效应。这涉及通过添加Boltzmann-和Landau型的碰撞操作员来修改Vlasov-Maxwell系统。这项工作的主要目的是研究Landau阻尼的研究，其中长期行为规定了线性化vlasov方程的初始值问题。在相对论的情况下找到最佳衰减率的工作已经完成，在这种情况下，有效性范围受碰撞效应的限制限制。现在将重点放在理解非同性主义环境中的衰变上。还将对Vlasov-Einstein系统进行研究，以包括一个完全相对论的模型，以解决恒星动态问题。这项工作很重要，因为它与宇宙审查制度有关。部分微分方程构成了物理世界数学建模的基础。数学分析的作用并不是创建方程，而是提供有关解决方案的定性和定量信息。这可能包括有关独特性，光滑和成长的问题的答案。此外，分析通常会开发出解决这些近似值准确性的解决方案和估计值的方法。 ***