On the Eigenvalues of Spectral Gaps of Elliptic PDEs on Waveguides

A method of calculating eigenvalues in the spectral gaps of self-adjoint elliptic partial differential equations on waveguides is presented. It is based on approximating the problem using domain truncation methods together with dissipative perturbation technique to the self-adjoint operator. The theoretical results essentially rely on the error estimate of Dirichlet-to-Neumann maps on the cross-section. The numerical examples show the efficiency of this approach.