I am learning Mean value property (MVP) of the heat equation. MVP of Laplace equation was relatively easy to understand I think it is because of the spherical symmetry. But I am not able to appreciate the MVP of heat equation. It's not very easy to imagine the "heat ball".
I would be glad for any kind of help.
My questions are
- How do I define a heat ball?
- How does it actually look like?
Text that i am following is as follows : http://www.math.ualberta.ca/~xinweiyu/527.1.08f/lec13.pdf (theorem 9)