A. Aslanyan and E.B. Davies
Separation of variables in perturbed cylinders
(544K, postscript)

ABSTRACT.  We study the Laplace operator subject to Dirichlet boundary conditions 
in a two-dimensional domain that is one-to-one mapped onto a cylinder 
(rectangle or infinite strip). As a result of this transformation the 
original eigenvalue problem is reduced to an equivalent problem for 
an operator with variable coefficients. Taking advantage of the simple 
geometry we separate variables by means of the Fourier decomposition 
method. The ODE system obtained in this way is then solved numerically 
yielding the eigenvalues of the operator. The same approach allows us 
to find complex resonances arising in some non-compact domains. We 
discuss numerical examples related to quantum waveguide problems.