Mathematical Sciences: Stochastic Partial Differential Equations

点击翻译按钮获取中文摘要

The principal investigator will study partial differential equations with random noise terms. Such equations often arise when physical systems are influenced by noise. This work will consider qualitative properties of solutions in the nonlinear case. There are several goals of this project. The first would involve the carrying over of the coupling technique from the field of infinite particle systems to stochastic partial differential equations. Another goal is the development of Ito's formula for the heat equations with a noise term. Also, propagation of singularities would be studied for random hyperbolic equations.