How to Approach Solving a 2D Damped Wave Equation?

[igor_b]

Hi to all!

I need to solve following equation:
$$\frac{\partial^2 u}{\partial t^2} + 2 \beta \frac{\partial u}{\partial t} -c^2\nabla^2u=0$$

It describes a damped wave on a x-y plane. $$2\beta$$ is damping factor and c is wave speed.

I haven't had any luck finding a PDE class that looks like this. Closest match is Helmholtz equation but it doesn't have $$\frac{\partial}{\partial t}$$ element.

Tried to solve it using Mathematica but didn't have any luck (but that is maybe because of the fact that I don't really know how to use Mathematica).

Any hints on how to proceed would be appreciated either on manual solving or by using Mathematica (or Matlab, for that matter).

Igor

 

[jrosen13]

separation of variables to turn it into ordinary differential equations. It looks like __ equation for spatial part, and __ for time part, but I won't fill in the blanks, that's cheating :)