Solve The PDE

Nah, I will not solve your problem for you mainly because this is a math help forum. If you want help then tell us where you are having trouble and show us the work that you have done so far.
 
Please show us what you have tried and exactly where you are stuck.

Please share your work/thoughts about this problem.
 
Please study:

Laplace's equation for heat transfer or diffusion. It is not the same problem - but it will give you ideas about your problem.
 
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