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Famous PDEs, diffusion equation

The diffusion equation whose one-dimensional version reads \begin{equation} \tag{2} \frac{\partial^2 u}{\partial x^2}=A\frac{\partial u}{\partial t}, \end{equation} and A is in this case called the diffusion constant. It can be used to model a wide selection of diffusion processes, from molecules to the diffusion of heat in a given material.