I am stuck with the start of this question:
The water table height in the region between two rivers equilibrates over a long time 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 diusion-like equation:
dh/dt = k(d^2*h)/(d*x^2) (The d is actually the partial squiggly d thing)
The river level was initially -H, however this changes instantaneously to a level of h(0; t) = h(L; t) = 0.
How do I find the initial conditions h(x,0)? (and in terms of a Fourier sine series?)
I'm stuck as the next part talks about seperating the variables to find h(x,t), does this mean I do not seperate variables in the first part? If so, what is the method for that? And how does that affect the second part?
Annoying as after these parts the majority of the question is routine
Claims damages because he didn't get a first