Mathematical Sciences: Reaction-Diffusion Equations: Asymptotic Problems, Random Perturbations, Probabilistic Approach

首席研究员是微扰理论和反应扩散方程领域的主要研究者。他在动力系统的小随机扰动方面做了基础工作，他的许多结果仍然是该领域当前研究的基石。该项目提出了20个难以解决的问题。主题涉及随机过程和偏微分方程。应用的主要领域出现在工程和生物学。特别是，研究者将探索偏微分方程与马尔可夫过程的关系。将研究无限维动力系统和半流的随机摄动。

The principal investigator is a leading researcher in the area of perturbation theory and reaction diffusion equations. He has done fundamental work on small random perturbations of dynamical systems and many of his results continue to be a corner stone in the current research in the field. The project proposes 20 hard and unsolved problems. The subject matter involves both stochastic processes and partial differential equations. The major areas of application arise in engineering and biology. In particular, the investigator will explore the relationships of partial differential equations with Markov processes. Random perturbations of infinite dimensional dynamical systems and semiflows will be studied.