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Heat Diffusion Equation and Standard Heat Equation

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November 8th, 2022

A) Let the temperature u inside a solid sphere be a function only of radial distance r from the center and time t. Show that the equation for heat diffusion is now: {see attachment}. This is not an exercise in doing a polar coordinate transformation. First you should derive an integral form for the equation by integrating over an appropriate domain. Then from this obtain the differential equation.
b) Show that a transformation of the form {see attachment} for a suitable choice of m can be used to reduce this equation to the standard heat equation

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