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I want to solve the heat PDE in a 1D domain for a source moving at constant speed. The problem has been solved already, the solution being stationary in a reference frame moving with the source.

This is highly un-intuitive, and I suppose the result originate from the fact the source is assumed to have been moving (exisiting) for an infinite amount of time.

Instead, I am interested in a source starting to move at time zero.

I attacked the problem as reported in the attachment, I wonder if the solution is correct.

Many thanks as usual for your help. I apologize for not writing the equation directly here, but I have not figured out yet how to use Latex in the post, I am getting there though.

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# Heat Equation with moving source

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