This award supports travel for participants in the "Conference on Hyperbolic Conservation Laws and Continuum Mechanics," held 12-14 May 2011 at Brown University. The workshop brings together leading theorists in conservation laws and in continuum mechanics, and aims to stimulate work at the interface between these fields and to inform young researchers about recent developments in the area.

The workshop will enhance communication among junior and senior researchers in conservation laws and continuum mechanics. Conference proceedings will be published in the Quarterly of Applied Mathematics of the American Mathematical Society. The conference encourages and supports participation by graduate students, junior researchers, and members of under-represented groups.

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Project Report

This conference was focused on mathematical theories that have impact on a great variety of scientific endeavors, including the mechanics of extended systems, elastic and plastic materials, the dynamics of gases and fluid mechanics. In these days of specialization it is becoming progressively more difficult to bring about communication between diverse groups of scientists. Participants were brought together from many leading research institutions. They included a large number of students and post-doctoral associates, who are in their early stages of their careers. Research findings are in the process of being published in the Quarterly of Applied Mathematics. Continuum mechanics is a scientific area with well developed mathematical theory and important applications to engineering. The theory of hyperbolic conservation laws has been developed in conjunction with applications to gas dynamics, magnetohydrodynamics, nonlinear elasticity and traffic theory. In recent years we have witnessed the exploration of new connections with subjects such as the kinetic theory of gases, plasma physics, the mathematical theory of semiconductors and general relativity. Breakthroughs in shock wave theory have taken place in the past decade, resolving classical open problems in gas dynamics, such as shock reflection on wedges, and gas flow in nozzles. New models and applications of conservation laws for instance to traffic problems. Another area of application is viscosity in viscoelastic polymers.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
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Henry A. Warchall
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Brown University
United States
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