Mathematical Sciences: Parabolic Partial Differential Equations in Nonsmooth Domains.

该项目将研究具有粗糙边界的域中的抛物型偏微分方程。 使用热方程的最新结果作为参考框架，将努力建立高阶抛物线方程和非圆柱域解的正则性质。 要处理的主要问题是域的谱性质和迹半群的性质。 除了解决微分方程中的基本问题外，该项目的结果还对概率、物理和工程等应用领域产生影响。 特别是胶体和秘密材料方面的问题可能会从这项投资中受益。

This project will study parabolic partial differential equations in domains with rough boundaries. Using as a frame of reference recent results on the heat equation, efforts will be made to establish regularity properties of solutions to higher order parabolic equations and noncylindrical domains. Main issues to be dealt with are the spectral properties of the domains and properties of the trace semigroup. In addition to solving basic questions in differential equations, the result of this project have implications to applied areas such as probability, physics and engineering. In particular problems in colloids and furtive materials might benefit from this investment.