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 is either the nonlinear von Kármán plate equation or the linear plate equation. In the latter case we also obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation.

Large time existence for thin vibrating plates

Mora, M. G.;
2011-01-01

Abstract

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 is either the nonlinear von Kármán plate equation or the linear plate equation. In the latter case we also obtain a convergence rate of the three-dimensional solution to the solution of the two-dimensional linear plate equation.
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11571/363575
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 12
  • ???jsp.display-item.citation.isi??? 12
social impact