Talk:Diffusion equation

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Feynman gives the diffusion equation (Volume II 3-4) as

\frac{\partial\phi}{\partial t} = k\nabla^2\phi

Is this equivalent? Or should it be added? It is more understandable to me at a high school level.

I think we should do this too, it's much more recognizable. Isn't this:
\frac{\partial\phi}{\partial t}=\nabla\cdot D(\phi)\nabla\phi(\vec{r},t)
just the same as this:
\frac{\partial\phi}{\partial t}=D(\phi)\nabla^2\phi(\vec{r},t)
In that case, the latter form is much preferred. For example, this is how Diffusion equation at scienceworld.wolfram.com puts it.
— Sverdrup 23:50, 18 November 2005 (UTC)
They are not equivalent, since
\nabla\cdot D(\phi)\nabla\phi(\vec{r},t) = (\nabla D(\phi)) \cdot (\nabla\phi(\vec{r},t)) + D(\phi)\nabla^2\phi(\vec{r},t).
However, if the diffusion coefficient D is a constant, say k, then we do get the equation
\frac{\partial\phi}{\partial t} = k\nabla^2\phi.
The latter equation is treated at heat equation.
In fact, the case where D is constant (or at least independent of φ) is very common. So it might be better to redirect diffusion equation to heat equation and move this article to nonlinear diffusion equation. -- Jitse Niesen (talk) 20:39, 20 November 2005 (UTC)
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