# Heat Equation with moving source

1. Oct 23, 2012

### 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.

#### Attached Files:

• ###### Green solution for the Heat equation over an infinite 1D domain and initial condition G.pdf
File size:
41.7 KB
Views:
89
2. Oct 23, 2012

### Staff: Mentor

Looks fine.

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

3. Oct 23, 2012

### muzialis

Many thanks for looking at it and the hint.

4. Oct 23, 2012

### 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 :

#### Attached Files:

• ###### Integral.JPG
File size:
36.6 KB
Views:
128
5. Oct 23, 2012

### muzialis

JJaquelin,

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

Cheers