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Thin vibrating plates: long time existence and convergence to the von Kármán plate equations
Author(s) -
Abels H.,
Mora M.G.,
Müller S.
Publication year - 2011
Publication title -
gamm‐mitteilungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.239
H-Index - 18
eISSN - 1522-2608
pISSN - 0936-7195
DOI - 10.1002/gamm.201110015
Subject(s) - convergence (economics) , zero (linguistics) , nonlinear system , mathematical analysis , mathematics , bending of plates , plate theory , physics , thermodynamics , boundary value problem , bending , quantum mechanics , linguistics , philosophy , economics , economic growth
The asymptotic behavior of the solutions of three‐dimensional nonlinear elastodynamics in a thin plate is studied, as the thickness h of the plate tends to zero. We discuss the long time existence and convergence to solutions of the time‐dependent von Kármán and linear plate equation under appropriate scalings of the applied force and of the initial values in terms of h (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)