Non-hom heat eq. w/ Dirichlet + Neumann BC

BangJensen

I'm trying to find the analytical solution to the following equation:

c1*d2p/dz2-dp/dt = -c2*cos(omega*t)

where
- p is a function of spatial z and time t, p=p(z,t)
- d2p/dz2 is the second derivative of p wrt z
- dp/dt is the first derivative of p wrt t

c1, c2 and omega are constants.

Initial condition: p(z,0) = 0
Boundary condition 1: p(z,t) = 0 for z = 0
Boundary condition 2: dp/dt = 0 for z = d

Everywhere I have looked for solutions so far does not allow the combination of Dirichlet and Neumann boundary conditions or the spatial domain has to be infinite.

I hope someone can help here.

Thanks.

Dr Transport

Try Lebedev's book on applied math. Your problem can be done fairly easily.