Mathematical Sciences: New Numerical Methods for Conservation Laws. Application to Non-Standard Shocks

9502766勒弗洛赫这项工作由国家科学基金会教师早期职业发展奖支持。研究部分将重点研究非线性双曲守恒定律；这些定律对于描述从流体力学到材料科学(如多相流、界面传播)的大量连续介质力学问题至关重要。该计划将有两个主要目标：(1)对熵不连续解的非线性稳定性以及激波捕捉数值方法的设计和非线性分析提供新的见解；(2)有助于更好地理解物理科学中允许非标准冲击波的几个应用问题。教育部分将包括制定研究生课程，将研究成果传播到科学界，包括工业实验室，并指导学生的工作，强调与工程师和研究人员在物理科学方面的合作活动。国家科学基金会强烈鼓励学术人员的早期发展，既是教育工作者，也是研究者。学院早期职业发展(Career)计划是一个基础范围的计划，为初级教师在其整体职业发展的背景下提供支持。它在一个单一的计划中结合了对最广泛意义上的高质量研究和教育的支持，以及那些传统上在科学和工程领域代表性不足的人的充分参与。这一计划加强并强调了基金会对充分、平衡的学术事业发展的重视，包括研究和教育。

9502766 LeFloch This work is supported by a National Science Foundation Faculty Early Career Development Award. The research component will focus on the study of nonlinear hyperbolic conservation laws; these laws are essential to the description of a large number of problems in continuum mechanics, from fluid dynamics to material science (e.g., multiphase flows, propagation of interfaces). The plan will have two major goals: (1) to provide new insight on the nonlinear stability of entropy discontinuous solutions and on the design and nonlinear analysis of shock-capturing numerical methods and (2) to contribute to better understanding of several applied problems from physical sciences admitting non-standard shock waves. The education component will include curriculum development at the graduate level, disseminating the research into the scientific community, including industrial laboratories, and directing the work of students, emphasizing collaborative activities with engineers and researchers in the physical sciences. The National Science Foundation strongly encourages the early development of academic faculty as both educators and researchers. The Faculty Early Career Development (CAREER) Program is a Foundation- wide program that provides for the support of junior faculty within the context of their overall career development. It combines in a single program the support of quality research and education in the broadest sense and the full participation of those traditionally underrepresented in science and engineering. This program enhances and emphasizes the importance the Foundation places on the development of full, balanced academic careers which include both research and education.