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.