dc.contributor.author Chechkin, Gregory A. dc.contributor.author Mel'nyk, Taras A. dc.date.accessioned 2011-03-20T12:01:09Z dc.date.accessioned 2016-10-05T14:14:18Z dc.date.available 2011-03-20T12:01:09Z dc.date.available 2016-10-05T14:14:18Z dc.date.issued 2011-05-14 dc.identifier.uri http://publications.mfo.de/handle/mfo/1186 dc.description Research in Pairs 2009 en_US dc.description.abstract The asymptotic behavior (as $\varepsilon \to 0$) of eigenvalues and eigenfunctions of a boundaryvalue problem for the Laplace operator in a thick cascade junction with concentrated masses is investigated. This cascade junction consists of the junction's body and great number $5N = \mathcal{O}(\varepsilon^{-1})$ of $\varepsilon$-alternating thin rods belonging to two classes. One class consists of rods of finite length and the second one consists of rods of small length of order $\mathcal{O}(\varepsilon)$. The density of the junction is order $\mathcal{O}(\varepsilon^{-\alpha})$ on the rods from the second class (the concentrated masses if $\alpha >0$) and $\mathcal{O}(1)$ outside of them. In addition, we study the influence of the concentrated masses on the asymptotic behavior of these magnitudes in the case $\alpha=1$ and $\alpha \in (0,1)$. en_US dc.language.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2011,12 dc.title Asymptotic behavior of the eigenvalues and eigenfunctions to a spectral problem in thick cascade junction with concentrated masses en_US dc.type Preprint en_US dc.rights.license Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. de dc.rights.license This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. en dc.identifier.doi 10.14760/OWP-2011-12 local.scientificprogram Research in Pairs 2009 local.series.id OWP-2011-12 dc.identifier.urn urn:nbn:de:101:1-201104069917 dc.identifier.ppn 1650844700
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