Mathematical Sciences: Parabolic Partial Differential Equations in Nonsmooth Domains.

本专题将研究抛物型偏微分 粗糙边界域中的方程 作为一个框架， 参考热方程的最新结果，将努力 使建立更高的解决方案的正则性 阶抛物型方程和非圆柱域。 主要 要处理的问题是光谱特性的 域和迹半群的性质。 除了解决微分学中的基本问题外， 方程，这个项目的结果有影响， 应用领域，如概率，物理和工程。 在 胶体和隐秘材料中的特殊问题可能 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.