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

这项美国-巴西合作科学计划奖将支持来自不同机构的七名美国数学家的研究合作，由纽约州立大学石溪分校的布拉德利·普洛领导，与巴西纯粹与应用数学研究所（IMPA）的Daniel Marchesin领导的一个巴西小组合作。该奖还将支持两名美国数学家参加1993年7月在IMPA举行的偏微分方程讲习班。该研究项目旨在分析混合类型的守恒定律系统，这也是研讨会的一个重点。这些系统出现在几个科学领域，包括多相流、弹塑性和磁流体力学。该基金将资助四名美国数学家和三名美国研究生前往巴西，以及一名巴西研究生前往美国。研究人员将在他们之前关于非线性守恒律系统基本解的数学理论的基础上，包括稳定性和分岔。他们将使用这一理论来升级非线性波的通用计算机程序，以便在应用中出现更复杂的系统，例如提高石油采收率和弹性塑性。他们还将关注从这些解决方案的知识中发现的建模问题。美方将受益于与IMPA同行的互动，IMPA是动力系统的卓越中心。巴方将加强在应用数学方面的专业知识。

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.