Large Solutions to Systems of Nonlinear Equations

非线性方程组的大解

• 批准号: 0422888
• 负责人: Helge Jenssen
• 金额: $ 2.61万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2003
• 资助国家: 美国
• 起止时间: 2003-09-01 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0422888&HistoricalAwards=false
• 关键词: Large; Solutions; Systems; Nonlinear; Equations

NSF Award Abstract - DMS-0206631Mathematical Sciences: Large Solutions to Systems of Nonlinear EquationsAbstract0206631 JenssenThe object of this research is threefold. First, we seek a better understanding of solutions to systems of hyperbolic (inviscid) conservation laws that are large in either amplitude or variation. New examples of explosive behavior will be considered, as well as conditions preventing singular behavior. Next, we will consider the multi-dimensional Navier-Stokes equations for a compressible fluid and establish global existence of large solutions with spherical or cylindrical symmetry. Finally, we will consider flow describing combustion. This is modeled by the Navier-Stokes equations augmented by equations describing the chemical processes. In this case we are particularly interested in the stability of wave patterns.The work deals with mathematical analysis of solutions to nonlinear partial differential equations. The research will investigate systems of conservation laws, compressible fluid flow, and equations describing reactive flow. Much of the existing theory for such nonlinear equations applies only to small solutions. However, large solutions are of great interest in applications such as gas flow, combustion, and detonations, and study of these solutions requires new techniques that will be developed in this project.

NSF奖摘要-DMS -0206631数学科学：非线性方程系统的大型解决方案Abstract0206631这项研究对象的Jenssenthe是三倍。 首先，我们寻求更好地理解振幅或变化较大的双曲线（Inviscid）保护定律系统的解决方案。 将考虑爆炸性行为的新例子，以及防止奇异行为的条件。 接下来，我们将考虑可压缩流体的多维Navier-Stokes方程，并用球形或圆柱形对称性建立大型溶液的全球存在。 最后，我们将考虑描述燃烧的流动。 这是由通过描述化学过程的方程式增强的Navier-Stokes方程来建模的。 在这种情况下，我们对波模式的稳定性特别感兴趣。该工作涉及非线性偏微分方程解决方案的数学分析。 该研究将研究保护法，可压缩流体流以及描述反应流动的方程式的系统。 这种非线性方程的现有理论中的许多理论仅适用于小解决方案。 但是，大型解决方案在诸如气流，燃烧和爆炸之类的应用中具有极大的兴趣，并且对这些解决方案的研究需要该项目中将开发的新技术。