Separation of Variables And Wiener Hopf Techniques

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Separation of Variables And Wiener Hopf Techniques
Samuel Karp
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However in polar coordinates, we would have u(r, Tr) = f(r) -^(r, 0) = rg(r), and here the probl«ii has been broken up into two distinct one part problems. Thus the same state of affairs is a mixed boundary value problem when expressed in car- tesian coordinates, while in polar coordinates it is a simple boundary value problem, -29- Consider now a problem referring to an obstacle sltunted upon the X axie from x = to x = 1. We may have boundary conditions which, when ex- pressed in cartesians, w...ill read, u(x, 0) « f(x) -oo1 The first of these equations may be treated independently. The remaining pair constitute a two p^^-t mixed boundary value problem.
We realize also that the amployment of elliptic coordinates would lead to a simpl e boundary value problem here.


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