Eigenvalue asymptotics of long Kirchhoff plates with clamped edges
Asymptotic expansions are constructed for the eigenvalues and eigenfunctions of the Dirichlet problem for the biharmonic operator in thin domains (Kirchhoff plates with clamped edges). For a rectangular plate the leading terms are asymptotically determined from the Dirichlet problem for a second-ord...
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| Veröffentlicht in: | Sbornik. Mathematics 2019-04, Vol.210 (4), p.473-494 |
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| container_title | Sbornik. Mathematics |
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| creator | Bakharev, F. L. Nazarov, S. A. |
| description | Asymptotic expansions are constructed for the eigenvalues and eigenfunctions of the Dirichlet problem for the biharmonic operator in thin domains (Kirchhoff plates with clamped edges). For a rectangular plate the leading terms are asymptotically determined from the Dirichlet problem for a second-order ordinary differential equation, while for a -junction of plates they are determined from another limiting problem in an infinite waveguide formed by three half-strips in the shape of a letter and describing a boundary-layer phenomenon. Open questions are stated for which the method developed gives no answer. Bibliography: 33 titles. |
| doi_str_mv | 10.1070/SM9008 |
| format | Article |
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L. ; Nazarov, S. A.</creator><creatorcontrib>Bakharev, F. L. ; Nazarov, S. A.</creatorcontrib><description>Asymptotic expansions are constructed for the eigenvalues and eigenfunctions of the Dirichlet problem for the biharmonic operator in thin domains (Kirchhoff plates with clamped edges). For a rectangular plate the leading terms are asymptotically determined from the Dirichlet problem for a second-order ordinary differential equation, while for a -junction of plates they are determined from another limiting problem in an infinite waveguide formed by three half-strips in the shape of a letter and describing a boundary-layer phenomenon. Open questions are stated for which the method developed gives no answer. 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A.</creatorcontrib><title>Eigenvalue asymptotics of long Kirchhoff plates with clamped edges</title><title>Sbornik. Mathematics</title><addtitle>MSB</addtitle><addtitle>Sb. Math</addtitle><description>Asymptotic expansions are constructed for the eigenvalues and eigenfunctions of the Dirichlet problem for the biharmonic operator in thin domains (Kirchhoff plates with clamped edges). For a rectangular plate the leading terms are asymptotically determined from the Dirichlet problem for a second-order ordinary differential equation, while for a -junction of plates they are determined from another limiting problem in an infinite waveguide formed by three half-strips in the shape of a letter and describing a boundary-layer phenomenon. Open questions are stated for which the method developed gives no answer. Bibliography: 33 titles.</description><subject>asymptotic behaviour</subject><subject>Asymptotic series</subject><subject>boundary layer</subject><subject>Differential equations</subject><subject>dimension reduction</subject><subject>Dirichlet problem</subject><subject>Eigenvalues</subject><subject>eigenvalues and eigenfunctions</subject><subject>Eigenvectors</subject><subject>Kirchhoff plate</subject><subject>Ordinary differential equations</subject><subject>Rectangular plates</subject><issn>1064-5616</issn><issn>1468-4802</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNpt0EtLw0AUBeBBFKxVf8Og6C56J_PIZGlLfWCLi-p6mMyjTUk7MZMo_fdGIrjQ1b2Lj3PgIHRO4IZABrfLRQ4gD9CIMCETJiE97H8QLOGCiGN0EuMGAHhK5AhNZuXK7T501Tms435bt6EtTcTB4yrsVvi5bMx6HbzHdaVbF_Fn2a6xqfS2dhY7u3LxFB15XUV39nPH6O1-9jp9TOYvD0_Tu3liKMg2Ec5SoJpJ7oyRee5TJmzhc5IVwntnSKGpBWppIRn31ha8sIJxokHLAtKcjtHlkFs34b1zsVWb0DW7vlKllGc8B8l5r64HZZoQY-O8qptyq5u9IqC-91HDPj28GGAZ6t-kP-jqH7RYTlTaS6ZYRlVtPf0C4DZuwQ</recordid><startdate>20190401</startdate><enddate>20190401</enddate><creator>Bakharev, F. L.</creator><creator>Nazarov, S. A.</creator><general>London Mathematical Society, Turpion Ltd and the Russian Academy of Sciences</general><general>IOP Publishing</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>7U5</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>KR7</scope><scope>L7M</scope></search><sort><creationdate>20190401</creationdate><title>Eigenvalue asymptotics of long Kirchhoff plates with clamped edges</title><author>Bakharev, F. L. ; Nazarov, S. A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c308t-6ed303a485ecc899f246dbf917b6ffec1ba3d03d3b845fddb5bd6451a0a8b0293</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>asymptotic behaviour</topic><topic>Asymptotic series</topic><topic>boundary layer</topic><topic>Differential equations</topic><topic>dimension reduction</topic><topic>Dirichlet problem</topic><topic>Eigenvalues</topic><topic>eigenvalues and eigenfunctions</topic><topic>Eigenvectors</topic><topic>Kirchhoff plate</topic><topic>Ordinary differential equations</topic><topic>Rectangular plates</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bakharev, F. L.</creatorcontrib><creatorcontrib>Nazarov, S. 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Math</addtitle><date>2019-04-01</date><risdate>2019</risdate><volume>210</volume><issue>4</issue><spage>473</spage><epage>494</epage><pages>473-494</pages><issn>1064-5616</issn><eissn>1468-4802</eissn><abstract>Asymptotic expansions are constructed for the eigenvalues and eigenfunctions of the Dirichlet problem for the biharmonic operator in thin domains (Kirchhoff plates with clamped edges). For a rectangular plate the leading terms are asymptotically determined from the Dirichlet problem for a second-order ordinary differential equation, while for a -junction of plates they are determined from another limiting problem in an infinite waveguide formed by three half-strips in the shape of a letter and describing a boundary-layer phenomenon. Open questions are stated for which the method developed gives no answer. 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| ispartof | Sbornik. Mathematics, 2019-04, Vol.210 (4), p.473-494 |
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| language | eng |
| recordid | cdi_iop_journals_10_1070_SM9008 |
| source | IOP Publishing Journals; Alma/SFX Local Collection |
| subjects | asymptotic behaviour Asymptotic series boundary layer Differential equations dimension reduction Dirichlet problem Eigenvalues eigenvalues and eigenfunctions Eigenvectors Kirchhoff plate Ordinary differential equations Rectangular plates |
| title | Eigenvalue asymptotics of long Kirchhoff plates with clamped edges |
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