Boundary Value Problems
For a disk with a radius of "c", let the polar coordinates be , and
, boundary condition.
continuity of potential.
continuity of derivative.
The solution as a product of two independent functions. By substitution into the above PDE we have:
The constant may be greater than , equal to or less than zero.
Use the continuity conditions and try to determine something more about A, B and λ.
Before choosing, apply the second boundary condition:
The continuity of the derivative provides a second condition:
If either A or B are zero then also must hold. So all we need is which implies . Remember
Example of Potential equation on semi-annulus.[edit | edit source]
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