PECASE: Systems of Conservation Laws and Related Models in Applied Sciences - Math Awareness and Outreach

University Of Maryland, College Park, College Park MD

Investigators

Abstract

Proposal Title: PECASE: SYSTEMS OF CONSERVATION LAWS AND RELATED MODELS IN APPLIED SCIENCES - MATH AWARENESS AND OUTREACH Institution: University of Maryland College Park The research program of the investigator lies on the interface between continuum physics and applied partial differential equations, with emphasis on nonlinear systems of conservation laws. These quasilinear systems in divergence form govern a broad spectrum of physical phenomena in compressible fluid dynamics, nonlinear materials science, particle physics, semiconductors, combustion, multi-phase flows, astrophysics, and other applied areas. In recent years, major progress has been made in both the theoretical and the numerical aspects of this field. The main objective of this investigation is to build a bridge between the most recent developments in the general mathematical theory and significant areas of application that have developed in the last few years. The main focus of this program will be given to significant and, until recently, unexplored areas of research, including: hyperbolic systems of conservation laws with large initial data; multi-dimensional systems in nonlinear elasticity, fluid dynamics, and combustion theory; vanishing viscosity solutions to models of compressible flows; stability of boundary layers for realistic models of compressible fluids; and analysis of numerical schemes for hyperbolic conservation laws. Advances in this interdisciplinary research will rely substantially on the development of new analytical techniques in nonlinear partial differential equations. Analytical and numerical methods in this field have developed together; analytical understanding contributes to the construction of accurate and efficient numerical schemes, while numerical experiments often lead the theoretical analysis. Progress in this research program will contribute (a) to the successful investigation of a wide variety of important physical systems modeled by conservation laws and (b) to the design of high performance computational algorithms. The investigator integrates into her work educational activities that demonstrate the importance of applied mathematics in a broad spectrum of sciences. Special emphasis is given to applications in materials sciences, biology, finance, and cutting edge technologies. The planned educational activities include programs for high school students, undergraduates, and graduate students. The investigator works to increase the diversity in the mathematical sciences by encouraging under-represented groups to study applied mathematics and choose it as a career. This project was originally funded as a CAREER award, and was converted to a Presidential Early Career Award for Engineers and Scientists (PECASE) award in September 2004.