U.S.-France Cooperative Research: Nonlinear Geometric Optics

9314095劳赫这个为期三年的奖项支持密歇根大学的杰弗里·B·劳赫和雷恩大学的盖伊·梅特维尔在应用数学方面的美法合作研究。其他法国调查人员是波尔多大学的J.L.Joly和同样来自雷恩大学的Christophe Cheverry。该奖项还将支持美国研究生和博士后研究人员的参与。这项研究的目的是发现和分析新的真正的非线性行为。他们将学习双曲型非线性偏微分方程组的短波长解。这些方程模拟了波的传播问题。然后，他们建议构造近似解，当波长趋于零时，其百分比误差趋于零。该项目汇集了在偏微分方程式和数学分析领域拥有专业知识的美国和法国调查人员。他们在非线性行为方面的工作将促进我们对这一领域的理解，并对激光物理中的非线性光学问题以及可压缩流体动力学问题有重要的应用。非线性光学问题对于高能激光器的设计至关重要。***

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. ***