It is generally known that the solutions of deterministic and stochastic differential equations （SDEs） usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventual...It is generally known that the solutions of deterministic and stochastic differential equations （SDEs） usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventually blow up or explode in finite time. If the drift and diffusion functions are globally Lipschitz, linear growth may still be experienced, as well as a possible blow-up of solutions in finite time. In this paper, a nonlinear scalar delay differential equation with a constant time lag is perturbed by a multiplicative Ito-type time - space white noise to form a stochastic Fokker-Planck delay differential equation. It is established that no explosion is possible in the presence of any intrinsically slow time - space white noise of Ito - type as manifested in the resulting stochastic Fokker- Planck delay differential equation. Time - space white noise has a role to play since the solution of the classical nonlinear equation without it still exhibits explosion.展开更多
对白噪声驱动随机系统的Fokker-Planck方程进行约化,求得约化方程的解析解,使用局部解析解和 Monte Carlo结合方法求解常系数Fokker-Planck方程,并与常系数Eokker-Planck方程的精确解进行对比, 之后求解了变驱动力系统的行为．数值模拟...对白噪声驱动随机系统的Fokker-Planck方程进行约化,求得约化方程的解析解,使用局部解析解和 Monte Carlo结合方法求解常系数Fokker-Planck方程,并与常系数Eokker-Planck方程的精确解进行对比, 之后求解了变驱动力系统的行为．数值模拟结果表明,有限解析／Monte Carlo结合的方法,能成功求解-维 Fokker-Planck方程,求解粒子数为105个,能获得十分光滑的PDF分布曲线,计算颗粒在300个时,就能获得较好的均值．其研究为两相湍流PDF模型新计算方法研究提供基础．展开更多
文摘It is generally known that the solutions of deterministic and stochastic differential equations （SDEs） usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventually blow up or explode in finite time. If the drift and diffusion functions are globally Lipschitz, linear growth may still be experienced, as well as a possible blow-up of solutions in finite time. In this paper, a nonlinear scalar delay differential equation with a constant time lag is perturbed by a multiplicative Ito-type time - space white noise to form a stochastic Fokker-Planck delay differential equation. It is established that no explosion is possible in the presence of any intrinsically slow time - space white noise of Ito - type as manifested in the resulting stochastic Fokker- Planck delay differential equation. Time - space white noise has a role to play since the solution of the classical nonlinear equation without it still exhibits explosion.
文摘本文利用一种新方法对Fokker- Planck方程的非古典势对称群生成元进行研究,找到方程的几个非古典势对称群生成元,并采用非古典对称群方法由这些对称群生成元构造得到Fokker- Planck方程的相应显式解.这些新显式解不能由Fokker -Planck方程本身的Lie对称或Li-e B cklund对称来获得.在验证所求得显式解的过程中,还发现并得到了另外几个显式解.这些新显式解则不能由Fokker -Planck方程本身的Lie对称,Lie- B cklund对称或非古典势对称来获得.文章表明,通过偏微分方程的非古典势对称群生成元来寻找其显式解是可能的.
