2 5 2 Consider U X Y Satisfying Laplace S Equation Inside A Rectangle 0 X L 0 Y H Subject To The Boundary C 1 (231.32 KiB) Viewed 31 times
2.5.2. Consider u(x, y) satisfying Laplace's equation inside a rectangle (0 < x < L, 0 < y <H) subject to the boundary conditions ди ду ди (0, ) = 0, 2 (x, 0) = 0 (,y ди (L, y) = 0, вы (1, H) = f(x). = ди . = ду
*(a) Without solving this problem, briefly explain the physical condition under which there is a solution to this problem. (b) Solve this problem by the method of separation of variables. Show that the method works only under the condition of part (a). (Hint: You may use (2.5.16) without derivation.] (c) The solution (part (b)] has an arbitrary constant. Determine it by consideration of the time-dependent heat equation (1.5.11) subject to the initial condition vib uu, y,0) = g(x,y).
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