@MISC{Aslanyan_separationof, author = {A. Aslanyan and E. B. Davies}, title = {Separation Of Variables In Perturbed Cylinders}, year = {} }

Share

OpenURL

Abstract

. We study the Laplace operator subject to Dirichlet boundary conditions in a two-dimensional domain that is one-toone 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. 1. Introduction The object of this study is the Dirichlet Laplacian in a perturbed cylinder, i.e. a domain that is mapped onto a rectangle or an infinitely long strip depending on the domain being compact or non-compact. A typical example of a perturbed cylinder is a waveguide where the propagation of wa...