U.S.-Brazil Cooperative Research: Studies on the Tricomi Operator and Operators of Mixed Type

巴罗斯-Neto0124940这一美国-巴西项目奖将为罗格斯大学的Jose Barros-Neto博士和巴西累西腓联邦大学的Fernando Cardoso博士之间的合作研究提供支持。研究人员打算研究一类偏微分方程的基本解，这类偏微分方程因其作为气体动力学和流动的数学模型的实用性而受到广泛的研究和推广。更具体地说，这个项目涉及Tricomi方程的基本解的研究，它是混合型偏微算子的经典原型，以及它在某些空间点上的推广。基于某些超几何函数在寻找Tricomi算子基本解中的重要作用，研究人员致力于发展关于混合型微分算子的新的分析事实，并将标准欧几里得分析推广到具有更复杂对称结构的高维流形。

Barros-Neto0124940This U.S.-Brazil Program award will provide support for cooperative research between Dr. Jose Barros-Neto of Rutgers University and Dr. Fernando Cardoso at the Universidade Federal do Recife in Brazil. The researchers intend to study fundamental solutions to a class of partial differential equations that have been the subject of extensive studies and generalizations for their usefulness as a mathematical model in gas dynamics and flows.More specifically, this project involves the study of fundamental solutions of the Tricomi equation, which is the classical prototype of a partial differential operator of mixed type, and its generalizations at certain spatial points. Building on the important role that certain hypergeometric functions play in the finding of fundamental solutions to the Tricomi operator, the researchers aim to develop new analytic facts about differential operators of mixed type and push forward standard Euclidean analysis to higher dimensional manifolds with more complicated symmetry structure.