Infinitely Differentiable Functions and the Heat Equation

by Michael R. Mitchell

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A proof that there exist infinitely differentiable but nonanalytic solutions of the heat equation. (A solution of the heat equation represents the temperature at a point x at a given time t of a homogeneous, heat-insulated rod of infinite length in which all points of a cross-section are at the same temperature at a given instant.) However, the solution found is not unique, and some of the results obtained by the method given are not physically realistic.

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