Davies E.B., Parnovski L.
Trapped modes in acoustic waveguides.
(450K, ps)

ABSTRACT.  We consider the Laplace operator acting on the infinite cylinder
with an obstacle inside it. Boundary conditions are assumed to
be Neumann. We study the existence of (embedded) eigenvalues in 
two cases. For two-dimentional symmetric obstacle we give both 
necessary and sufficient conditions for the existence of an 
eigenvalue. For thin nonsymmetrical obstacle parallel to the
axis of the cylinder we prove that an eigenvalue always exists.