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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?

Thanks in advance, cheers.

Marco