Consider Laplaces equation inside a rectangle 0 x L, 0 y H, with the boundary conditions
Chapter 2, Problem 2.4.23(choose chapter or problem)
Consider Laplaces equation inside a rectangle 0 x L, 0 y H, with the boundary conditions u x(0, y)=0, u x(L, y) = g(y), u y (x, 0) = 0, u y (x, H) = f(x). (a) What is the solvability condition and its physical interpretation? (b) Show that u(x, y) = A(x2 y2) is a solution if f(x) and g(y) are constants [under the conditions of part (a)]. (c) Under the conditions of part (a), solve the general case [nonconstant f(x) and g(y)]. [Hints: Use part (b) and the fact that f(x) = fav + [f(x) fav], where fav = 1 L L 0 f(x) dx.]
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