dc.contributor.author Čečkin, Grigorij A. dc.contributor.author Mel'nyk, Taras A. dc.date.accessioned 2012-07-03T12:00:01Z dc.date.accessioned 2016-10-05T14:14:24Z dc.date.available 2012-07-03T12:00:01Z dc.date.available 2016-10-05T14:14:24Z dc.date.issued 2012-07-03 dc.identifier.uri http://publications.mfo.de/handle/mfo/1213 dc.description Research in Pairs 2012 en_US dc.description.abstract The asymptotic behavior (as $\varepsilon \to 0$) of eigenvalues and eigenfunctions of a boundary- value problem for the Laplace operator in a thick cascade junction with concentrated masses is studied. This cascade junction consists of the junction’s body and a great number $5N = \mathcal(\varepsilon^{−1})$ 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 of order $\mathcal{O}(\varepsilon^{−\alpha})$ on the rods from the second class and $\mathcal{O}(1)$ outside of them. There exist five qualitatively different cases in the asymptotic behavior of eigenvibrations as $\varepsilon \to 0$, namely the cases of “light” concentrated masses ($\alpha \in (0, 1)$), “middle” concentrated masses ($\alpha = 1$), “slightly heavy” concentrated masses ($\alpha \in (1, 2)$), “intermediate heavy” concentrated masses ($\alpha = 2$), and “very heavy” concentrated masses ($\alpha > 2$). In the paper we study the influence of the concentrated masses on the asymptotic behavior of the eigen-magnitudes if $\alpha \in (1, 2)$. en_US dc.language.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2012,10 dc.title Spatial-Skin Effect for a Spectral Problem with "Slightly Heavy" Concentrated Masses in a Thick Cascade Junction 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-2012-10 local.scientificprogram Research in Pairs 2012 local.series.id OWP-2012-10 local.subject.msc 35 local.subject.msc 47 local.subject.msc 74 dc.identifier.urn urn:nbn:de:101:1-201207047549 dc.identifier.ppn 1651532222
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