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666 CHAPTER 18 The Potential Equation

∂u
10. Write an expression for the solution of the following (0, y) = 0for y ≥ 0
Neumann problem for the lower half-plane: ∂x
∂u
2
∇ u(x, y) = 0for −∞ < x < ∞, y < 0 ∂y (x,0) = f (x) for x ≥ 0
∂u 12. Solve the following mixed-boundary value problem:
(x,0) = f (x) for −∞ < x < ∞
∂y
2
∇ u(x, y) = 0for x > 0, y > 0
11. Solve the following Neumann problem for the right u(0, y) = 0for y ≥ 0
quarter-plane:
∂u
(x,0) = f (x) for x ≥ 0
2
∇ u(x, y) = 0for x > 0, y > 0 ∂y

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October 14, 2010 15:27 THM/NEIL Page-666 27410_18_ch18_p641-666