Study on stochastic partial differential equations with singular coefficients

奇异系数随机偏微分方程的研究

• 批准号: 21654021
• 负责人: FUNAKI Tadahisa
• 金额: $ 2.16万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Challenging Exploratory Research
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21654021/
• 关键词: 確率論; 解析学; 確率偏微分方程式

We have studied the nonequilibrium fluctuation limit for the motion of two dimensional Young diagrams from the aspect of interface model. The limit is described by a certain stochastic partial differential equation. Moreover, the equilibrium solution of the equation which describes the growth of interfaces in consideration of the random fluctuation effect in space and time, the stochastic entropic solution of the stochastic partial differential equation with fractional differential operators, blow-up problem in a harmonic map heat flow, the singular limit of anisotropic Allen-Cahn equations and precise estimates on the position of the interfaces are studied.

我们从界面模型的角度研究了二维杨氏图运动的非平衡涨落极限。该极限由某个随机偏微分方程描述。此外，考虑空间和时间上的随机涨落效应的描述界面增长的方程的平衡解、带有分数微分算子的随机偏微分方程的随机熵解、调和映射热中的爆炸问题研究了流动、各向异性 Allen-Cahn 方程的奇异极限和界面位置的精确估计。

项目成果

Threshold and generic type I behaviors for a supercritical nonlinear heat equation

超临界非线性热方程的阈值和通用 I 类行为

• DOI: 10.1016/j.jfa.2011.02.025
• 发表时间: 2011
• 作者: H.Matano

An application of braid group theory to the finite time dead-core rate

辫群理论在有限时间死核率中的应用

• 发表时间: 2010
• 作者: J.;C.
• 通讯作者: C.

A variational problem associated with the minimal speed of travelling waves for sPatially periodic reaction-diffusion equations

空间周期性反应扩散方程与行波最小速度相关的变分问题

• 发表时间: 2010
• 作者: X.Liang; H.Matano
• 通讯作者: H.Matano

Stochastic analysis on large scale interacting systems

大规模交互系统的随机分析

• 发表时间: 2009
• 作者: T.Funaki

Hydrodynamic limit for interacting systems

相互作用系统的流体动力学极限

• 发表时间: 2011
• 作者: 舟木直久