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ON THE SPECTRUM OF AN ELASTIC SOLID WITH CUSPS
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
St Petersburg State University, Russia.
2016 (English)In: Advances in Differential Equations, ISSN 1079-9389, Vol. 21, no 9-10, 887-944 p.Article in journal (Refereed) Published
Abstract [en]

The spectral problem of anisotropic elasticity with traction free boundary conditions is considered in a bounded domain with a spatial cusp having its vertex at the origin and given by triples (x(1), x(2), x(3)) such that x(3)(-2)(x(1), x(2)) is an element of omega, where w is a two-dimensional Lipschitz domain with a compact closure. We show that there exists a threshold lambda(t) amp;gt; 0 expressed explicitly in terms of the elasticity constants and the area of w such that the continuous spectrum coincides with the half-line [lambda(t), infinity), whereas the interval [0, lambda(t)) contains only the discrete spectrum. The asymptotic formula for solutions to this spectral problem near cusps vertex is also derived. A principle feature of this asymptotic formula is the dependence of the leading term on the spectral parameter.

Place, publisher, year, edition, pages
KHAYYAM PUBL CO INC , 2016. Vol. 21, no 9-10, 887-944 p.
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-136236ISI: 000394480300003OAI: oai:DiVA.org:liu-136236DiVA: diva2:1086212
Note

Funding Agencies|Russian Foundation for Basic Research [15-01-02175]; Linkoping University (Sweden); Swedish Research Council (VR)

Available from: 2017-03-31 Created: 2017-03-31 Last updated: 2017-03-31

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