Asymptotic Problems for Stochastic Processes and PDE's

小行星9803522 本计画将研究哈密尔顿系统的扰动。这种扰动系统的长期行为，即使扰动是纯粹确定性的， 应该用与汉密尔顿函数相关的图上的随机过程来描述。一 一类偏微分方程的渐近问题，例如 平面Navier-Stokes方程或反应扩散的小扩散渐近性 在不可压缩流体中，与哈密顿量的随机扰动密切相关 系统.概率的方法是有用的，在分析这些问题。 研究了受随机噪声扰动的动力系统的长时间行为 在这个项目中。这种类型的问题出现在许多应用中，例如， 宇宙物体的行为或具有小粘度的流体的运动。的 扰动，即使它们很小，对于长期的行为是必不可少的。 系统渐近的方法，这是研究人员正在开发的项目，是 最有希望分析这类问题的方法。

9803522 Freidlin Perturbations of the Hamiltonian systems will be studied in this project. The long- time behavior of such perturbed systems, even if the perturbations are purely deterministic, should be described by a stochastic process on a graph related to the Hamilton function. A class of asymptotic problems for PDEs, such as the small viscosity asymptotics for the Navier-Stokes equations in the plane or small diffusion asymptotics for reaction - diffusion in an incompressible fluid, are closely related to random perturbations of the Hamiltonian systems. The probabilistic approach is useful in analyzing these problems. Long time behavior of dynamical systems perturbed by a stochastic noise is studied in this project. This type of problem arises in many applications, for example, the long time behavior of cosmic objects or the motion of a fluid with a small viscosity. The perturbations, even if they are small, become essential for the long-time behavior of the system. The asymptotic approach, which the investigator is developing in the project, is the most promising for analyzing this type of problem.