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Surface waves and scattering by unbounded obstacles

Presented by: 
D Yafaev Université de Rennes 1
Date: 
Wednesday 25th March 2015 - 10:00 to 11:00
Venue: 
INI Seminar Room 1
Abstract: 
Consider the Laplace operator $H=-\Delta$ in the exterior $\Omega$ of a parabolic region in ${\bf R}^d$, and let $H_{0}=-\Delta$ be the operator in the space $L^2 ({\bf R}^d)$. The wave operators for the pair $H_{0}$, $H$ exist for an arbitrary self-adjoint boundary condition on $\partial\Omega$. For the case of the Dirichlet boundary condition, the wave operators are unitary which excludes the existence of surface waves on $\partial\Omega$. For the Neumann boundary condition, the existence of surface waves is an open problem, and we are going to discuss it.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons