Mathematical Sciences: Smoothing Estimates for Null Forms

mms -9501096 Machedon将研究各种非线性波动方程的适定性问题。特别地，讨论了在最小的数据规则假设下的存在性、唯一性和规则性问题。使用研究者和S. Klainerman开发的新型平滑估计来解决这些问题。偏微分方程是物理世界数学建模的基础。数学分析的作用与其说是创建方程，不如说是提供关于解的定性和定量信息。这可能包括回答关于独特性、平滑性和增长性的问题。此外，分析常常发展出解的近似方法和对这些近似精度的估计。

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.