Singularities of the scattering kernel for several convex obstacles (Q910948)

Let \({\mathcal O}\) be a compact set with a smooth boundary in \({\mathbb{R}}^ n\) (n\(\geq 2)\) such that \(\Omega ={\mathbb{R}}^ n,{\mathcal O}\) is connected. The author studies the scattering problem \[ \square u(t,x)=(\partial^ 2_ t-\Delta_ x)u(t,x)=0\quad in\quad {\mathbb{R}}^ 1\times \Omega,\quad \partial_{\nu}u(t,x)=0\quad on\quad R^ 1\times \partial \Omega, \] \[ u(0,x)=f_ 1(x),\quad and\quad \partial_ tu(0,x)=f_ 2(x)\quad on\quad \Omega, \] where \(\nu\) is the unit inner normal to the boundary. He uses Neuman boundary conditions, and analyzes the sing supp S(\(\cdot,- w,w)\) when \({\mathcal O}\) consists of several disjoint convex obstacles \(\{\) \({\mathcal O}_ j\}\).