I. Bihari, A generalization of a lemma of bellman and its application to uniqueness problems of differential equations, Acta Mathematica Academiae Scientiarum Hungaricae, vol.23, issue.6, pp.81-94, 1956.
DOI : 10.1007/BF02022967

A. M. Il, Matching of asymptotic expansions of solutions of boundary value problems, volume 102 of Translations of Mathematical Monographs, 1992.

P. Joly and A. Semin, Construction and analysis of improved kirchhoff conditions for acoustic wave propagation in a junction of thin slots, ESAIM Proceedings, pp.44-67, 2008.

P. Joly and A. Semin, Propagation of an acoustic wave in a junction of two thin slots, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00335588

P. Joly and S. Tordeux, Matching of Asymptotic Expansions for Wave Propagation in Media with Thin Slots I: The Asymptotic Expansion, Multiscale Modeling & Simulation, vol.5, issue.1
DOI : 10.1137/05064494X

URL : https://hal.archives-ouvertes.fr/inria-00527588

P. Kuchment, Graph models for waves in thin structures. Waves Random Media, pp.1-24, 2002.

J. Rubinstein and M. Schatzman, Variational Problems??on Multiply Connected Thin Strips I:??Basic Estimates and Convergence??of the Laplacian Spectrum, Archive for Rational Mechanics and Analysis, vol.160, issue.4, pp.271-308, 2001.
DOI : 10.1007/s002050100164

J. Rubinstein and M. Schatzman, Variational Problems??on Multiply Connected Thin Strips II:??Convergence of the Ginzburg-Landau, Archive for Rational Mechanics and Analysis, vol.160, issue.4, pp.309-324, 2001.
DOI : 10.1007/s002050100165

A. Semin, Numerical resolution of the wave equation on a network of slots, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00411825

M. Van-dyke, Perturbation Method in Fluid Mechanics, Journal of Applied Mechanics, vol.43, issue.1, 1964.
DOI : 10.1115/1.3423785

.. Matching, 18 2.3.1 Modal expansion of solutions, 18 2.3.2 Derivation of the matching conditions . . . . . . . . . . . 23

U. Existence and .. Of-the-formal-expansion, 26 3.1.1 Restriction to a bounded domain, p.32

I. Analysis and .. Kirchhoff-conditions, 43 4.2.1 Asymptotic expansions, p.46