Abels, Helmut ; Mora, Maria Giovanna 
; Müller, Stefan
Alternative Links zum Volltext:DOIVerlag
| Dokumentenart: | Artikel |
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| Titel eines Journals oder einer Zeitschrift: | Communications in Partial Differential Equations |
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| Verlag: | TAYLOR & FRANCIS INC |
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| Ort der Veröffentlichung: | PHILADELPHIA |
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| Band: | 36 |
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| Nummer des Zeitschriftenheftes oder des Kapitels: | 12 |
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| Seitenbereich: | S. 2062-2102 |
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| Datum: | 2011 |
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| Institutionen: | Mathematik > Prof. Dr. Helmut Abels |
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| Identifikationsnummer: | | Wert | Typ |
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| 10.1080/03605302.2011.618209 | DOI |
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| Stichwörter / Keywords: | NONLINEAR ELASTICITY; CONVERGENCE; EQUATIONS; SYSTEMS; Dimension reduction; Nonlinear elasticity; Plate theory; Singular perturbation; Von Karman; Wave equation |
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| Dewey-Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
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| Status: | Veröffentlicht |
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| Begutachtet: | Ja, diese Version wurde begutachtet |
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| An der Universität Regensburg entstanden: | Ja |
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| Dokumenten-ID: | 65366 |
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Zusammenfassung
We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large times under appropriate scaling of the initial values such that the limit system as h -> 0 is either the nonlinear von Karman plate equation or the linear fourth order Germain-Lagrange ...
Zusammenfassung
We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large times under appropriate scaling of the initial values such that the limit system as h -> 0 is either the nonlinear von Karman plate equation or the linear fourth order Germain-Lagrange equation. In the case of the linear Germain-Lagrange equation we even obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation.
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