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The heat equation for a function $I(x, y, t)$ of three variables $x$, $y$ (the coordinates) and $t$ (the time) is defined as follows
\begin{align}
\frac{\partial I}{\partial t}
&= \alpha\left(\frac{\partial^2I}{\partial x^2}+\frac{\partial^2I}{\partial y^2}\right) \\
&= \alpha \operatorname{div}(\nabla I)
\end{align}
where $\alpha$ is a real ...
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