Scattering Solutions in Networks of Thin Fibers: Small Diameter Asymptotics
نویسندگان
چکیده
منابع مشابه
Scattering Solutions in Networks of Thin Fibers: Small Diameter Asymptotics
Small diameter asymptotics is obtained for scattering solutions in a network of thin fibers. The asymptotics is expressed in terms of solutions of related problems on the limiting quantum graph Γ. We calculate the Lagrangian gluing conditions at vertices v ∈ Γ for the problems on the limiting graph. If the frequency of the incident wave is above the bottom of the absolutely continuous spectrum,...
متن کاملar X iv : m at h - ph / 0 60 90 21 v 1 8 S ep 2 00 6 Scattering solutions in a network of thin fibers : small diameter asymptotics
Small diameter asymptotics is obtained for scattering solutions in a network of thin fibers. The asymptotics is expressed in terms of solutions of related problems on the limiting quantum graph Γ. We calculate the Lagrangian gluing conditions at vertices v ∈ Γ for the problems on the limiting graph. If the frequency of the incident wave is above the bottom of the absolutely continuous spectrum,...
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Our talk at Lisbon SAMP conference was based mainly on our recent results on small diameter asymptotics for solutions of the Helmgoltz equation in networks of thin fibers. These results were published in [21]. The present paper contains a detailed review of [21] under some assumptions which make the results much more transparent. It also contains several new theorems on the structure of the spe...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2007
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-007-0220-8