Hello there, 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.