spherical diffusion

• To: mathgroup at smc.vnet.net
• Subject: [mg15727] spherical diffusion
• From: Bernd Brandt <bernd at bio.vu.nl>
• Date: Fri, 5 Feb 1999 03:42:23 -0500 (EST)
• Organization: VU Biology, Amsterdam, The Netherlands
• Sender: owner-wri-mathgroup at wolfram.com

```Hi,

Does anyone know how to solve a spherical diffusion equation with
Mathematica?
This equation is part of a larger problem and has to be solved
numerically. Here it includes a hyperbolic consumption term.

X0 is the diffusing substrate.
Derivative[1,0][ X0][0,t] == 0 because of the spherical symmetry. Of
course starting with r=0 gives 1/0 -> infinity...

Is it possible to solve this problem with NDSolve?

NDSolve[{D[X0[r,t],t] ==
D[r^2*D*D[X0[r, t], r], r]/r^2 - (IM*X1*X0)/(K0 + X0), X0[r,1] == 5,

X0[10,t]==X0, Derivative[1,0][ X0][0.0001,t] == 0}, X0,
{r,0.0001,10},{t,1,10}]

Thanks,

Bernd

```

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