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# Trouble With Partial Differentiation Watch

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1. I've been given this question, but am stuck on the very first part, which is annoying as I can probably do the rest!:

The water table height in the region between two rivers equilibrates over long times to the water level in the rivers. The axis OX measures the lateral distance between the two rivers, with x = 0 corresponding to the left river and x = L corresponding to the right river. The water table height at position x at time t is given by h(x, t), measured with respect to ground level. The water table height obeys a diffusion-like equation:

du/dt = k(d^2*u)/(d*x^2) (The d is actually the squiggle for partials)

The river level changes from an initial depth of -H, instantaneously, to a level of
h(0, t) = h(L, t) = 0.

However, I cannot find the initial conditions h(x,0) (expressed as a Fourier sine series). (Which is the first part of the question).

The question pretty much states to not use the separation of the variables method until the next part, hence I am stuck :O

Thank you

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Updated: December 17, 2010
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