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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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