Evolution Of The Concentration Of Particles PDE

Available identifiers

MaRDI QIDQ6775461

spatiotemporal evolution of the concentration of particles depending on the position and time

Description

This is a nonlinear, nonlocal Fokker-Planck equation that is also called McKean-Vlasov PDE or aggregation-diffusion equation.

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Defining Formula: ${\partial }_{t}c(x,t)={\partial }_x(c(x,t)(F^{\prime }*c(\cdot ,t))(x))+\frac{{\sigma }^2}{2}{\partial }_{xx}c(x,t)$

$(F^{\prime }*c(\cdot ,t))$ symbol represents Convolution Between Interaction Force And Density

$F^{\prime }$ symbol represents Interaction Force

$\sigma$ symbol represents Diffusion Coefficient

$c$ symbol represents Concentration Of Particles

$t$ symbol represents Time

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