Heat Equation with moving source

[muzialis]

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.

 

[mfb]

Looks fine.

You can use LaTeX with the [itex] (inline) and [tex] (new line) commands (or shorter: $equation$ and $$equation$$)

 

[muzialis]

Many thanks for looking at it and the hint.

 

[JJacquelin]

Hi muzialis !

Sorry, I have not the time to dactylography the whole solution.
If there is no mistake, the key points are in attachment :

 

[muzialis]

JJaquelin,

what to say, you reda my mind! Many thanks for this, hope to be able to help back some time

Cheers