How do you evaluate the first and the second moment for 1,2,3 dimensions?

 

I attached a picture with the equation.

Edited November 17, 201411 yr by radamel7

This looks like the Greens Function solution by introducing the linear diffusion operator, L

[math]L = \frac{\partial }{{\partial t}} - k{\nabla ^2}[/math]

 

 

Have you considered the boundary conditions, both in time and space?

No, I guess no boundary conditions in this case.

In regards to the Green's function comment, a table of common Green's functions can be found here: http://en.wikipedia.org/wiki/Green%27s_function#Table_of_Green.27s_functions. (Yours is on there.) Additionally, at a glance it should be easy to see that it looks very much like a wave equation. In fact, it looks nearly identical to the Schrodinger equation, except that's it's real everywhere. Should you have no knowledge of Green's functions you could try to solve it by analogy with wave equations.