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，其中包括纽约州立大学石溪分校的布拉德利·普洛尔，由里约热内卢理论与应用数学研究所(IMPA)的Daniel Marchesin领导的一个巴西小组。该奖项还将支持两名美国数学家参加1993年7月在IMPA举行的偏微分方程式研讨会。该研究项目旨在分析混合类型的守恒法系统，这也将是讲习班的一个重点。这些系统存在于几个科学领域，包括多相流、弹塑性和磁流体动力学。资金将支持4名美国数学家和3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工作的基础上，建立包括稳定性和分叉在内的非线性守恒律系统基本解的数学理论。他们将利用这一理论来升级非线性波的通用计算机程序，以允许在应用中出现的更复杂的系统中使用，例如提高石油采收率和弹塑性。他们还将重点关注从此类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.