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Random heat evolution problem
A metal bar of length 1 lies along the unit interval. Its temperature distribution is given by $$g(x)=4x^2−1x.$$ At time $t=0$, its left end is set to temperature 2 and its right end to 0. Here is my (tentative) sketch the temperature distribution at times $t=0$, $t=0.01$, $t=0.1$, and $t=10$.
