Title: Kinetic limit for a wave equation in a randomly perturbed medium
Abstract:
This talk will present a convergence result for the scalar wave equation
\begin{equation}
\frac{\partial^2}{\partial t^2}u(x,t)=c(x)^2\Delta u(x,t)
\end{equation}
with a nonconstant, randomly perturbed speed of wave propagation $c(x)$.
Its fluctuations are of order $\sqrt{\eps}$ with $\mathcal{O}(1)$ correlation length.
The method of graph expansions is used to analyze the $\eps\rightarrow0$ limit
behavior of the averaged Wigner function.
It is shown that on macroscopic ($\mathcal{O}\left(\eps^{-1}\right)$)
space and time scales the disorder-averaged Wigner function converges
to the solution of a Boltzmann equation.