| 陈涌,高洪俊,郭柏灵.带随机初值的随机偏微分方程整体解的存在性[J].数学年刊A辑,2011,32(5):545~564 |
| 带随机初值的随机偏微分方程整体解的存在性 |
| The Existence of a Global Solution to Stochastic Partial Differential Equation with Random Initial Conditions |
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| DOI： |
| 中文关键词: 随机偏微分方程 格林函数 Kolmogorov准则 随机初值 |
| 英文关键词:Stochastic partial differential equation Green's function Kolmogorov's criterion Random initial condition |
| 基金项目:国家自然科学基金(No.10871097,No.11028102); 江苏省高校自然科学基金(No.11KJA110001); 江苏省高校“青蓝工程”资助的项目 |
| Author Name | Affiliation | E-mail | | CHEN Yong | Institute of Mathematics,School of Mathematical Science,Nanjing Normal University,Nanjing 210046,China. | youngchen329@126.com | | GAO Hongjun | Institute of Mathematics,School of Mathematical Science,Nanjing Normal University,Nanjing 210046,China. | gaohj@njnu.edu.cn | | GUO Boling | Institute of Applied Physics and Computational Mathematics,Beijing 100088,China. | gbl@iapcm.ac.cn |
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| 中文摘要: |
| 研究了一类带随机初值并且由分数次Brownian运动驱动的随机偏微分方程. 借助于Kolmogorov准则,
建立了整体Lipschitz条件下此类随机偏微分方程的一个解. 同时证明了局部Lipschitz条件下整体解的存在性. |
| 英文摘要: |
| This paper deals with a class of stochastic partial differential equations (SPDEs) driven by fractional Brownian motion with random initial conditions.
Based on Kolmogorov's criterion, the authors construct a solution to the SPDEs with global Lipschitz conditions.
Simultaneously, the existence of the global solution is proved under local Lipschitz conditions. |
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