U.S.-Brazil Coooperative Science Program: New Developments in Nonlinear Conservation Laws

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This US-Brazil Cooperative Science Program award will support research collaboration by seven US mathematicians from various institutions, led by Bradley Plohr of the State University of New York at Stony Brook, with a Brazilian group led by Daniel Marchesin of the Pure and Applied Mathematics Institute (IMPA) in Rio de Janeiro. The award will also support participation by two US mathematicians in a July 1993 Workshop on Partial Differential Equations, held at IMPA. The research project aims to analyze mixed-type systems of conservation laws, which will also be a focus of the Workshop. These systems occur in several scientific areas, including multiphase flow, elastoplasticity, and magnetohydrodynamics. Funds will support travel to Brazil by four US mathematicians and three US graduate students, as well as travel to the US by a Brazilian graduate student. The researchers will build on their previous work on the mathematical theory of fundamental solutions of nonlinear systems of conservation laws, including stability and bifurcation. They will use this theory to upgrade the general computer program for nonlinear waves, to allow use in more complicated systems that arise in applications, such as enhanced oil recovery and elastoplasticity. They will also focus on modelling issues uncovered from knowledge of such solutions. The US side will benefit from interaction with counterparts at IMPA, which is a center of excellence in dynamical systems. The Brazilian side will strengthen their expertise in applied mathematics.