| 带随机初值的随机偏微分方程整体解的存在性 |
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| 引用本文： | 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(中文版),2011,32(5):545-564. |
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| 作者姓名： | 陈涌 高洪俊 郭柏灵 |
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| 作者单位： | 南京师范大学数学科学学院数学研究所;北京应用物理与计算数学研究所; |
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| 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 |
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| 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.
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| 关 键 词： | 随机偏微分方程 格林函数 Kolmogorov准则 随机初值 |
The Existence of a Global Solution to Stochastic Partial Differential Equation with Random Initial Conditions |
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| CHEN Yong,GAO Hongjun and GUO Boling.The Existence of a Global Solution to Stochastic Partial Differential Equation with Random Initial Conditions[J].Chinese Annals of Mathematics,2011,32(5):545-564. |
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| Authors: | CHEN Yong GAO Hongjun and GUO Boling |
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| Institution: | CHEN Yong~1 GAO Hongjun~1 GUO Boling~2 1 Institute of Mathematics,School of Mathematical Science,Nanjing Normal University,Nanjing 210046,China. 2 Institute of Applied Physics and Computational Mathematics,Beijing 100088,China. |
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| Abstract: | 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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| Keywords: | Stochastic partial differential equation Green's function Kolmogorov's criterion Random initial condition |
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