$$ \newcommand{\uex}{{u_{\small\mbox{e}}}} \newcommand{\Aex}{{A_{\small\mbox{e}}}} \newcommand{\half}{\frac{1}{2}} \newcommand{\tp}{\thinspace .} \newcommand{\Oof}[1]{\mathcal{O}(#1)} \newcommand{\dfc}{\alpha} % diffusion coefficient $$

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Damping of a discontinuity; problem

Problem.

Two pieces of a material, at different temperatures, are brought in contact at \( t=0 \). Assume the end points of the pieces are kept at the initial temperature. How does the heat flow from the hot to the cold piece?

Or: A huge ion concentration on one side of a synapse in the brain (concentration discontinuity) is released and ions move by diffusion.

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