Mathematical Sciences: Conservation Laws that Change Type

8903768 KEYFITZ这个项目涉及非经典的严格双曲型守恒律系统的数学性质和应用。具有这些特殊特征的模型可以用来描述连续介质力学中的各种复杂流动，包括粘弹性和粘塑性流体，在流体和固体弹性中经历相变的混合物中的流动，以及多孔介质流动；类似的方程也出现在颗粒流的模型中。在最近的研究中，首席研究人员已经确定了一些区分不同模型的数学特性；这些特性包括波速的分离程度、类型改变时的速度行为以及波曲线的其他定性特性。她计划研究这些性质如何影响适定性，并研究高阶扰动下解的稳定性。还将研究出现在具体应用中的模型，结论，包括数值计算的算法，将应用于多维守恒定律。

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.