For the following wave equation

$ \frac{{\partial ^2 p}}{{\partial ^2 x}} + \frac{{\partial ^2 p}}{{\partial ^2 y}} = A\frac{{\partial ^2 p}}{{\partial ^2 t}} + B\frac{{\partial p}}{{\partial t}} $

is there a way to show that there are boundary conditions at or near positive and negative infinity, for both non-zero B and B=0 conditions, and for {A,B} as rational numbers? I believe that this should follow from Sommerfeld's condition of radiation, and should perhaps be similar to conditions for the ordinary wave equation. What are these boundary conditions? Ideally, I think that the boundary conditions should involve both time and spatial derivatives.

By "positive and negative infinity" I mean that I am interested in what happens when $x \to \pm \infty $ and $y \to \pm \infty$. I've been working on a problem where I would like to computationally solve the wave equation with boundary conditions that approximate infinity. So I suppose that this would be an imposed compatibility condition.

imposedcompatibility condition to restrict the set of solutions for a PDE? $\endgroup$ – Willie Wong Jul 24 '10 at 9:21