Mathematical Sciences: Nonlinear Evolution Equations II

本课题将研究非线性色散方程解的存在性和正则性。要考虑的主要问题是奇点的发展，解的寿命，以及热弹性方程解的爆破。所采用的技术主要来自于对换向子的谐波分析和先验估计。要分析的问题是在物理和工程现象的方程建模中的最先进的数学问题。

This project will study existence and regularity of solutions for nonlinear dispersive equations. The main topics to be considered are the development of singularities, the life span of solutions, and blow up of solutions to thermoelasticity equations. The techniques to be employed come mainly from harmonic analysis and apriori estimates for commutators. The questions to be analyzed are state of the art mathematical problems in equations modeling phenomena in physics and engineering.