In a (bounded) domain $\Omega \subset \mathbb{R}^n$, if we're studying the Laplace equation or heat equation or such PDE's we can impose the Dirichlet
$u|\_{\partial\Omega} \equiv 0$,
Neumann 
$D\_{\nu} u|\_{\partial\Omega}\equiv 0$
or Robin (for $\alpha \in \mathbb{R}$) 
$(D\_{\nu} u + \alpha u)|\_{\partial \Omega} \equiv 0$.


I know that, for example for the heat equation, Dirichlet eigenvalues correspond physically to the boundary being in contact with a (large) heat bath at $T=0$. Or, in the Laplace equation, if we're interested in the modes supported by $\Omega$ (as a drum), Dirichlet boundary conditions can be thought of keeping the boundary from moving.


Neumann boundary conditions, for the heat flow, correspond to a perfectly insulated boundary. For the Laplace equation and drum modes, I think this corresponds to allowing the boundary to flap up and down, but not move otherwise.




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My question is: what sort of physical interpretations are there for the Robin boundary conditions? [Wikipedia](http://en.wikipedia.org/wiki/Robin_boundary_conditions) says that they are related to electromagnetic problems, but gives no details. I'd be happy with answers that are not necessarily physics-related, for example, if there was somewhere that Robin boundary conditions naturally arise in a mathematical context, I'd be interested to know about that as well.



Physical interpretation of Robin boundary conditions
Here is an example where $\Omega = \mathbb{R}^3$. One way to establish dispersion for the wave equation involves taking a temporal Fourier transform. In order to do this one has to multiply by a cutoff function supported in $t \in [0,\infty)$. 
You then get the equation


$(\Delta+\omega^2)\psi = F$


where $\psi$ is the temporal Fourier transform of the product of the original solution with the cutoff, $\omega$ is the Fourier variable, and $F$ is a function controllable by initial data via a finite time energy inequality. If this plan of attack is going to work, we need to make sure that $\psi$ is uniquely determined by $F$. This of course requires appropriate boundary conditions at $\infty$. These turn out to be


1) $\psi = O\left(|x|^{-1}\right)$


2) $\frac{\partial\psi}{\partial r} - i\omega\psi = O\left(|x|^{-2}\right)$


This is a sort of Robin condition at infinity. See <http://terrytao.wordpress.com/2011/04/21/the-limiting-absorption-principle/> for more details.


