Analytical and Numerical Methods for Transport Equations

输运方程的分析和数值方法

• 批准号: 0104112
• 负责人: Guergana Petrova
• 金额: $ 8.17万
• 依托单位: Regents of the University of Michigan - Ann Arbor
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2001
• 资助国家: 美国
• 起止时间: 2001-08-01 至 2001-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0104112&HistoricalAwards=false
• 关键词: Analytical; Numerical; Methods; Transport; Equations

0104112PetrovaThis project addresses some problems in transport equations, Godunov type central schemes for hyperbolic conservation laws, classical and nonlinear approximation. The common thread that runs through the proposed research is the use of techniques from approximation theory, harmonic and functional analysis (Littlewood-Paley theory, wavelet decompositions, maximal functions, interpolation and K-functionals) to prove analytic results in other areas of applied mathematics and to use these techniques to develop numerical methods. Particular emphases will be placed on several issues: development of a satisfactory theory for linear transport equations in several space dimensions which arise when linearizing the nonlinear problem, development of Godunov type central schemes for solving multidimensional systems of conservation laws, and application of these schemes to various problems and models. Extensions of averaging lemmas to go from microscopic to macroscopic formulations will also be of primary concern. A portion of this project will address fundamental questions in nonlinear approximation and multivariate cubature.The areas under discussion (nonlinear approximation, analytical properties of solutions to transport equations and development of effective numerical methods for their computation) are of significant practical interest. The applications include image processing, statistical estimation, fluid mechanics, geophysics, meteorology, astrophysics, multi-component flows, ground water flow, semiconductors, and reactive flows.

0104112Petrovathis项目解决了运输方程中的一些问题，Godunov型中央计划的双曲线保护法，经典和非线性近似。通过拟议的研究运行的共同线程是使用近似理论，谐波和功能分析（Littlewood-Paley理论，小波分解，最大功能，互插和K功能）的技术，以证明在应用数学的其他领域以及开发这些技术方法中的其他领域。在几个问题上，将特别重点放在几个问题上：在几个空间维度中的线性传输方程开发令人满意的理论，这些方程在线性化非线性问题时会出现，戈德诺夫类型中心方案的开发用于解决多维保护法，以及这些方案在各种问题和模型中的应用。平均引理从显微镜变为宏观制剂的扩展也将引起主要问题。 该项目的一部分将解决非线性近似和多元立方体中的基本问题。所讨论的领域（非线性近似，解决方案解决方案的分析性能以及开发用于计算的有效数值方法）具有很大的实际利益。应用包括图像处理，统计估计，流体力学，地球物理学，气象，天体物理学，多组分流，地下水流，半导体和反应性流量。