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In this work we find a solution to problem of the heat equation which isannihiliated at a cubic boundary $f$. The solution turns out to be theconvolution between the fundamental solution of the heat equation and afunction $\phi$ which solves a third order ODE. However we believe that themain contribution is the procedure itself, which links in a ratherstraightforward way, solutions of the heat equation $v$ with moving boundaries$f$ through the convolution of the heat kernel with $\mathbb{C}^p$ funtions$\phi$.

A solution to the heat equation with a cubic moving boundary