Mathematical Sciences: Conservation Laws that Change Type

数学科学：改变类型的守恒定律

• 批准号: 8903768
• 负责人: Barbara Keyfitz
• 金额: $ 4.47万
• 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: 1989
• 资助国家: 美国
• 起止时间: 1989-05-15 至 1991-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8903768&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Conservation; Laws; Change

8903768 Keyfitz This project is concerned with the mathematical properties and applications of systems of conservation laws that are not of classical, strictly hyperbolic type. Models with these unusual features may be used to describe a variety of complex flows in continuum mechanics, including visco-elastic and visco-plastic fluids, flow in mixtures undergoing phase transitions in fluids and in solid elasticity, and porous-medium flows; similar equations appear in models for granular flows. In recent research, the principal investigator has identified some mathematical properties distinguishing different models; these include degree of separation of the wave speeds, behavior of the speeds where the type changes, and other qualitative properties of the wave curves. She plans to examine how these properties affect well-posedness, and to study stability of solutions under higher-order perturbations. Studies will also be made of models that appear in specific applications, and the conclusions, including algorithms for numerical computation, will be applied to multidimensional conservation laws.

8903768 凯菲茨 这个项目关注的是 和应用的守恒定律系统， 经典的严格双曲型 下演员 不寻常的特征可以用来描述各种复杂的 连续介质力学中的流动，包括粘弹性和 粘塑性流体，在经历相分离的混合物中的流动 流体和固体弹性的转变，以及 多孔介质流动;类似的方程出现在 颗粒流 在最近的研究中，首席研究员 已经发现了一些数学性质， 不同的模型;这些包括分离的程度 波速，类型变化时的速度行为，以及 波形曲线的其他定性性质。 她计划 研究这些属性如何影响适定性，并 研究高阶扰动下解的稳定性。 还将研究出现在特定环境中的模型， 应用程序和结论，包括算法， 数值计算，将适用于多维 守恒定律