POWRE: Research in Applied Analysis and Conservation Laws

POWRE：应用分析和守恒定律研究

• 批准号: 9973475
• 负责人: Barbara Keyfitz
• 金额: $ 3.57万
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-08-01 至 2000-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9973475&HistoricalAwards=false
• 关键词: POWRE; Research; Applied; Analysis; Conservation

The PI will use this grant as partial salary support for a sabbatical leave at Brown University, visiting mathematicians in the Mathematics and Applied Mathematics Departments.Research and scholarly activities planned for the period include preparing a monograph on nonstrictly hyperbolic conservation laws and conservation laws that change type. The proposer has worked extensively on problems in this area since 1976. Recognition of the possible utility of these models in engineering applications, along with continuing mathematical advances, has inspired this effort to bring together in one place the results of the proposer and of other researchers in the field, to broaden the scope of examples treated, and to make the subject accessible to practitioners in other fields. A major contribution of the book will be to introduce to mathematicians interested in the theory and numerical analysis of conservation lawsa number of interesting new prototype problems and applications. Some of the motivation for studying nonstrictly hyperbolic problems comes from elasticity and continuum mechanics. Other application areas that have furnished examples include flow through porous media (petroleum reservoirs) and multiphase flows (for example, mixtures of liquid and steam, bubbly liquids, and fluidized bed reactors) which are important in several fields of engineering and technology.Keyfitz also proposes to advance her recent research on multidimensional conservation laws, in cooperation with Dafermos, Strauss, and other Brown faculty. The lack of a good existence theory in more than one space dimension is the outstanding theoretical problem in quasilinear hyperbolic equations. One approach is through the study of self-similar problems. Results obtained so far by Canic and Keyfitz indicate that some basic questions in both elliptic and hyperbolic equations must be answered. Many aspects of nonlinear analysis may play a role here. Brown's mathematics department offers great strength in this area,both in its permanent faculty and in the visitors who have planned to be there in 1999-2000.In addition to the theoretical importance of existence questions, there is much applications interest in self-similar problems, which include such benchmark flows as shock reflection by a wedge.The POWRE grant offers the proposer focussed support for research and scholarship at a critical time, when she has been able to conclude some administrative and family responsibilities. It will also allow her to learn new methodologies (in nonlinear analysis) and to engage in cross-disciplinary study. The outcome, both in the form of the eventual book and in research advances in multidimensional conservation laws, will mark a significant increase in the proposer's research strength and visibility.

PI将把这笔赠款用作布朗大学休假的部分工资支持，访问数学和应用数学部门的数学家。该期间计划的研究和学术活动包括准备有关不可思议的超级保护保护法和逐渐变化的专着。 自1976年以来，该提议者一直在该领域的问题上进行了广泛的研究。认识到这些模型在工程应用中的可能实用性，以及持续的数学进步，启发了这一努力，将提案者和该领域的其他研究人员的结果汇集在一起​​，以扩大受试者的范围，以使受试者访问其他领域的范围，并在其他领域中访问了其他领域。 该书的主要贡献是向对保护法律的理论和数值分析感兴趣的数学家介绍许多有趣的新原型问题和应用。 研究非收紧双曲问题的一些动机来自弹性和连续机械。 提供示例的其他应用领域包括流过多孔介质（石油储层）和多相流（例如，液体和蒸汽的混合物，起泡的液体和流化的床反应堆）在工程和技术的几个领域都很重要。Keyfitz在多个研究中也提出了有关与Daimemensional Cancertional Cancertict Lawn in contercorts in Comporials in Comportscorts的跨性别的研究，并在DaiDapecerult和其他方面进行了促进。 在一个以上的空间维度中，缺乏良好的存在理论是准双曲线方程中的杰出理论问题。 一种方法是通过研究自相似问题。 到目前为止，Canic和KeyFitz获得的结果表明，必须回答椭圆形和双曲线方程中的一些基本问题。 非线性分析的许多方面可能在这里发挥作用。 布朗的数学部门在该领域具有很大的优势，无论是在其永久教师和计划在1999年至2000年到达那里的访客。除了存在的存在问题的理论重要性外，对自我类似问题的理论重要性有很大的应用，包括自我类似的问题，包括这样的基准流动，包括一项能够进行的研究，并在某些方面提供了良好的研究。行政和家庭责任。 这也将使她能够学习新方法（在非线性分析中）并从事跨学科研究。 以最终书籍的形式以及多维保护法的研究进展，结果都将标志着提议者的研究实力和可见性大幅提高。