PI: Machedon DMS-9501096 Machedon will study questions of well-posedness of various nonlinear wave equations. In particular, the question of existence, uniqueness and regularity under minimal assumptions of regularity of the data is addressed. These questions are approached using the new kind of smoothing estimates developed by the investigator and S. Klainerman. Partial differential equations form a basis for mathematical modeling of the physical world. The role of mathematical analysis is not so much to create the equations as it is to provide qualitative and quantitative information about the solutions. This may include answers to questions about uniqueness, smoothness and growth. In addition, analysis often develops methods for approximation of solutions and estimates on the accuracy of these approximations.
