Partial Derivative of a formula based on the height of a cylinder

[currently]

Homework Statement

Consider a cylinder of radius a and height H. The base of the cylinder is at z=0 and the top is at z=H. Find a function which satisfies ∂U/∂t = k(nabla)^2U in the domain and stated boundary conditions and initial conditions.

Relevant Equations

* ∂U/∂t = k∇^2U
* Boundary condition: U=0 on the surface of the cylinder at all times.
* Initial condition: U within the domain = α(r)β(z) at time t=0 where α(r)=e^-r

The function should use (r,z,t) variables
The domain is (0,H)

Since U is not dependent on angle, then theta can be ignored in the expression for Laplacian in cylindrical coordinates(?)

 

[vanhees71]

Yes, because also the boundary and initial conditions do not depend on ##\theta##, the problem is symmetric under rotations around the ##z##-axis. Then I'd try a separation ansatz since also the boundary and initial conditions separate into a product of ##r## and ##z##.

BTW: It would help very much, if you'd use the LaTeX features of the Forum software (MathJaX), because it makes the formulae much better readable:

https://www.physicsforums.com/help/latexhelp/