9314095 Rauch This three-year award supports U.S.-France cooperative research in applied mathematics between Jeffrey B. Rauch of the University of Michigan and Guy Metvier of the University of Rennes. Other French investigators are J.L. Joly, University of Bordeaux and Christophe Cheverry, also from the University of Rennes. The award will also support the participation of the U.S. graduate students and postdoctoral researchers. The objective of this research is to discover and analyze new genuinely nonlinear behaviors. They will study short wavelength solutions of nonlinear partial differential equations of hyperbolic type. These equations model problems of wave propagation. Then they propose to construct approximate solutions whose percent error tends to zero as the wavelength tends to zero. The project brings together U.S. and French investigators with expertise in the area of partial differential equations and mathematical analysis. Their work on nonlinear behaviors will advance our understanding of this area and also have important applications to problems of nonlinear optics in laser physics, which are crucial for the design of high energy lasers, and to problems in compressible fluid dynamics. ***
