Second order evolution equations with dynamic boundary conditions
type: Item
instance of: scholarly article
title: Second order evolution equations with dynamic boundary conditions
zbMATH Open document ID: 0854.34059
author: K. T. Andrews
author: K. L. Kuttler
author: M. Shillor
published in: Journal of Mathematical Analysis and Applications
publication date: 1997-01-22T00:00:00Z
review text: The authors establish an existence and uniqueness result for the second-order abstract Cauchy problem \((Bu)''+ (Mu)'+ Nu= f\), \(Bu(0)= Bu_0\), \((Bu)'(0)= Bu_1\), where the nonlinear operators \(M\) and \(N\) and the linear operator \(B\) are suitably restricted and map a Hilbert space into its dual. The result is shown to be directly applicable to weak formulations of certain initial-boundary value problems modelling the dynamic vibrations of rods and beams with attached tip masses at their free ends.
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 902473
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: second-order abstract Cauchy problem
zbMATH Keywords: Hilbert space
zbMATH Keywords: initial-boundary value problems
zbMATH Keywords: dynamic vibrations of rods and beams
reviewed by: Wilson Lamb
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0053
OpenAlex ID: W1998932774
DOI: 10.1006/JMAA.1996.0053
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description: scientific article; zbMATH DE number 902473