Evolution Of The Concentration Of Particles SPDE

Available identifiers

MaRDI QIDQ6775462

randomness is maintained by this stochastic equation also known as Dean-Kawasaki equation

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

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

$N$ symbol represents Number of Particles

$\sigma$ symbol represents Diffusion Coefficient

$\xi$ symbol represents White Noise

$c$ symbol represents Concentration Of Particles

$t$ symbol represents Time

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