Solve the Neumann problem for a rectangle: a2u a2u a x2 + ay2 = o, o < x < a, o < y < b
Chapter 13, Problem 21(choose chapter or problem)
Solve the Neumann problem for a rectangle: a2u a2u a x2 + ay2 = o, o < x < a, o < y < b au I = 0 au I = o. 0 < x < a ay y=o , ay y=b :: lx=O = O, :: lx=a = g(y), O < Y < b. (a) Explain why a necessary condition for a solution u to exist is that g satisfy rg(y)dy = o. This is sometimes called a compatibility condition. Do some extra reading and explain the compatibility condition on physical grounds. (b) If u is a solution of the BVP, explain why u + c, where c is an arbitrary constant, is also a solution.
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