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.