中科院数学与系统科学研究院

华罗庚数学研究中心

 

系列报告

 

 

报告人:Prof. Sergei Kuksin (法国巴黎7)

 

  目:Stochastic Burgers Equation

 

  间:2017.11.06(星期一),14:30-16:30N902

2017.11.08(星期三),14:30-16:30N902

2017.11.13(星期一),14:30-16:30N902

2017.11.15(星期三),14:30-16:30N902

2017.11.20(星期一),14:30-16:30N902

2017.11.22(星期三),14:30-16:30N902

2017.11.27(星期一),14:30-16:30N902

2017.11.29(星期三),14:30-16:30N902

 

Abstract

 

My course is dedicated to the stochastic Burgers equation under the periodic boundary conditions. This is a reach in properties nonlinear stochastic partial differential equation (SPDE) and a popular physical model. I will start with proving basic facts about the equation and defining the Markov process and the two Markov semigroups, related with it. This part of the course may be regarded as a brief introduction to SPDE. I will continue with more delicate qualitative properties of the equation, will use them to study the limits « time to infinity » and « viscosity to zero » and will explain the relevance of the two limits for physics.

I will assume only very basic knowledge of the probability (random variables and their distribution,  independent random variables, elementary facts about the Wiener process), and of the PDE (Sobolev spaces of functions of one variable, basics about the heat and the Laplace equation).

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