Stochastic analysis of fractal stochastic Burgers equation

2015 Fiscal Year Final Research Report

• Project/Area Number: 25800060
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Shinshu University
• Principal Investigator: XIE Bin 信州大学, 学術研究院理学系, 准教授 (50510038)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 確率解析 / 確率偏微分方程式 / entropy solution / intermittency / 分数冪ラプラスアン

Outline of Final Research Achievements

We mainly investigated the uniqueness and various properties to the solution of stochastic partial differential equations, by the approach of stochastic analysis. We first considered the uniqueness of stochastic fractal Burgers equations. By introducing a new kind of definition of solution, stochastic entropy solution, we proved the uniqueness of the solution in some proper state space. We also studied long time behavior relative to intermittency of stochastic reaction-diffusion equation driven by space-time white noise on a bounded domain, which are essentially depending on the estimate of its fundamental solution.

Free Research Field

確率解析