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du/dt = B d

^{2}u/dx

^{2}+ q(x,t) 0 < x < L, t > 0

Where q(x,t) is the source of heat.

The problem is, I want the heat source to be only at one end of the bar, but every example I find of this kind of problem has a heat source that is a function of x, which I don't understand, since the heat generated should be 0 for all x except x = 0, and I don't know how to deal with that.

Also, what do I do for the insulated boundary on the other side? I want the heat to continue to build without escaping.

This is so frustrating! Any help is greatly appreciated!!

ps. The actual problem I am trying to solve is to find the pressure P(x,t) in a 1D finite reservoir, with a constant source of water at one end, but as far as I can tell, this problem is analogous, and I figured more people would be familiar with the heat equation example.