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