Graph-like models for thin waveguides with Robin boundary conditions

2008/03/30 by C. Cacciapuoti, Claudio Cacciapuoti, Cacciapuoti, C. +3
Computer Science · Mathematics · Physics and Astronomy · #81Q15 #Advanced Mathematical Modeling in Engineering #FOS: Physical sciences #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics #math-ph #math.MP #msc:81Q15

paper · pdf · doi:10.48550/arxiv.0803.4314

27 pages, 2 figures; PDFLatex. Changed introduction and conclusions. Added references

openalex publication_date 2008/03/30 · arxiv created 2008/06/04 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss the limit of small width for the Laplacian defined on a waveguide with Robin boundary conditions. Under suitable hypothesis on the scaling of the curvature, we prove the convergence of the Robin Laplacian to the Laplacian on the corresponding graph. We show that the projections on each transverse mode generically give rise to decoupling conditions between the edges of the graph while exceptionally a coupling can occur. The non decoupling conditions are related to the existence of resonances at the thresholds of the continuum spectrum.

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