PDE's - Heat Flow - Examples

Hello everyone,

I am currently trying to learn PDE's and have some tricky heat flow
problems. Can anyone help me out?

Given the following:

du/dt (x,t) = d^2u/dt^2 (x,t) + e^-x, 0 < x < pi, t > 0

u(0,t) = u(pi,t) = 0, t > 0

u(x,0) = sin(2x), 0 < x < pi

Does anyone know what the physical interpretation of the given
initial-boundary value problem is?

Does anyone know any good practical examples of the heat equation in
engineering?

Thanks,
zSXD

.

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