We consider unbounded regions which consist of a bounded domain 풞 joined to an unbounded region ℰ by a tube T(ε) whose cross-section is of small diameter ε. On such a region, we consider the Laplacian with Neumann boundary conditions. We show that as ε → 0+, the spectral resonances converge to eigenvalues of 풞, resonances of ℰ, or eigenvalues for a two point boundary value problem on an interval of the same length as the tube. The main goal of our work is to give estimates for the rates of convergence.
|Number of pages||19|
|Journal||Journal of Differential Equations|
|State||Published - Jan 20 1995|
ASJC Scopus subject areas
- Applied Mathematics