Suppose one has the following PDE in (x,y):
a(x,y)*(fxx + fyy) + b(x,y)*fx = e(f), (1)
where fx= partial f/partial x, etc, and
where a(x=1,y) = 0, so that along the line x=1, the PDE becomes
b(1,y)*fx = e(f). (2)
Does condition (2) effectively serve as a boundary condition on the original PDE (1) to solve in the region x
Issam Kaddoura
Dear M. E. Sulkanen
I think there is something is missing.
This is not the right approach to create boundary conditions for the second-order PDE. For example:
If (x2 - 1)(fxx + fyy) + (x2 - y)fx = f2 (1)
According to your claim, If x=1, then
(1- y)fx = f2 is a boundary condition over the region x
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M. E. Sulkanen
Issam,
I'm not sure I understand. In your example we have
(1-y)fx = f2 is only true at x=1, not in the entire region.
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