Nonlinear Partial Differential Equations in Kinetic Theory

运动理论中的非线性偏微分方程

基本信息

批准号：
9876820
负责人：
Robert Glassey
金额：
$ 11.55万
依托单位：
Indiana University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
1999
资助国家：
美国
起止时间：
1999-07-01 至 2002-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9876820&HistoricalAwards=false
关键词：
Nonlinear Partial Differential Equations Kinetic

项目摘要

A "collisionless" plasma is a fully ionized gas in whichelectromagnetic forces dominate collisional effects. The motion of ahigh temperature, low density collisionless plasma is described bythe Vlasov-Maxwell equations, a nonlinear system of partialdifferential equations. The major question to be addressed is this:are there shocks in a collisionless plasma? That is, could asingularity develop from smoothly prescribed initial values as timeprogresses? Additionally, "induction heating" will be studied. Inthis area one investigates how a conductive material is heated byusing electromagnetic waves. Microwave heating is a particularexample."Plasmas" are often called the fourth state of matter (after solids,liquids and gases). Plasmas account for a huge proportion of thematerial in the universe. Famous examples of plasmas include thesolar wind, the ionosphere, galactic nebulae and comet tails. Themotion of a plasma is described by a number of complicated equationsdictated by physics. The mathematician's goal is to show that theseequations have solutions, at least under certain conditions. This isthe main thrust of the proposal. A completely different applicationto be studied is called "induction heating." Here one tries todetermine how various materials can be heated by passing electromagnetic waves through them. The microwave heating of food is a particular example.

“无碰撞”等离子体是一种完全电离的气体，其中电磁力占据了碰撞效应。 Ahigh温度，低密度无碰撞等离子体的运动由Vlasov-Maxwell方程（一种非线性方程式）描述。要解决的主要问题是：无碰撞血浆中是否有冲击？也就是说，Asingularity是否可以从平滑规定的初始值作为时代发展？另外，将研究“感应加热”。在这个地区，人们研究了如何通过电磁波加热导电材料。微波加热是一个特殊的样本。“等离子体”通常称为物质的第四个状态（固体，液体和气体之后）。等离子体在宇宙中占了很大一部分的材料。等离子体的著名例子包括乳腺风，电离层，银河星云和彗星尾巴。等离子体的主题是由物理学绘制的许多复杂方程来描述的。数学家的目标是表明，至少在某些条件下，这些问题具有解决方案。这是该提议的主要目的。研究的完全不同的应用称为“感应加热”。在这里，人们会尝试通过将电磁波通过它们加热各种材料。食物的微波加热是一个特殊的例子。