Classical Fokker Planck Equation

Available identifiers

WikidataQ891766 ScholiaQ891766MaRDI QIDQ6674263

partial differential equation describing the dynamics of a probability density of the velocity of a particle under the influence of drag forces and random forces

Description

For vanishing drift and constant diffusion, the Fokker Planck equation yield's Fick's first law of diffusion.
Note the external forcing which connects the FPE to the model order reduction and/or optimal control tasks.

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Defining Formula: $\frac{\partial }{\partial t}p(x,t)=-\frac{\partial }{\partial x}[(\mu (x,t)-u)p(x,t)]+\frac{{\partial }^2}{\partial x^2}[D(x,t)p(x,t)]$

$D$ symbol represents Diffusion Coefficient

$\mu$ symbol represents Drift (Velocity)

$p$ symbol represents Probability Distribution

$t$ symbol represents Time

$u$ symbol represents Control System Input

$x$ symbol represents Classical Position

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Related URL

https://en.wikipedia.org/wiki/Fokker%E2%80%93Planck_equation

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