3. Suppose that u(x. t) satisfies the diffusion equation
ut = kuxx
for 0 < x < L and t > 0, and the Robin boundary conditions ux(0, t) ? aou(0, t) = 0 and ux(L, t) + aLu(L, t) = 0
where k, L, a0 and aL are all positive constants.
Show that ... is a decreasing function of t.
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A Diffusion Equation with Energy Decreasing as a Function of Time is investigated. The solution is detailed and well presented.