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

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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.