The Kardar-Parisi-Zhang equation and universality class

随机偏微分方程（SPDE）在整个科学中被用来提供比 当随机性或不确定性存在时的偏微分方程。 然而，我们对这些问题的理解 方程处于原始阶段。 调查人员正在研究远远超出这一领域的有关例子 为了发展一种实用的SPDE理论， 最重要的例子是Kardar-Parisi-Zhang方程。 尽管该方程在物理学中被广泛用于模拟随机生长的界面， 人们对适定性知之甚少，也不知道解是什么样的。 在过去的几年里，调查人员 发现了几个确切的解决方案，这项研究的目的是建立在这些和揭示可积结构的 方程

Stochastic partial differential equations (SPDE) are used throughout the sciences to provide more precise models than partial differential equations when randomness or uncertainty are present. However, our understanding of these equation is in a primitive stage. The investigator is studying relevant examples which fall well out of the domain of present theory, in order to develop an applicable theory of SPDE. The most important example is the Kardar-Parisi-Zhang equation. Although the equation is widely used in physics to model randomly growing interfaces, very little was known about well-posedness, or what the solutions looked like. In the last few years, the investigator has discovered several exact solutions, and this research aims to build on these and uncover the integrable structure of the equation.