# Second Fick's law with nonconstant diffusion coefficient

Hello everybody.
I should solve a modified version of second Fick's law in nondimensional spherical coordinates; t is the time and rho [0,1] the nondimensional radius. In this equation the diffusion coefficient is vraiable with t and rho.

The equation is the following:

dC/dt = (1/rho^2)*d/d(rho)(rho^2*D(rho,t)*dC/d(rho))

Initial conditions:
C(0,rho) = a*rho^4 + b*rho^2 -(a + b);

Boundary conditions:
dC(t,0)/d(rho) = 0
C(t,1) = 0

Is it possible to solve such an equation by Laplace transforms?
Alternatively, is there a user friendly tool for numerical solution of a PDE like this?

Marco

Chestermiller
Mentor
I don't think an analytic solution exists. It would have to be solved numerically. I would just convert it to a set of ODE's using the method of lines, and then solve the equations numerically in FORTRAN using an automatic (stiff) integration package.

Chet

• mabiondi
Thanks a lot for the suggestion, I really appreciate it. I'll try to develop a routine using MOL.
Cheers,
Marco