Spectral analysis and limit behaviours in a spring-mass system

M. Pellicer; J. Solà-Morales

doi:10.3934/cpaa.2008.7.563

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2008, Volume 7, Issue 3: 563-577. Doi: 10.3934/cpaa.2008.7.563

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Spectral analysis and limit behaviours in a spring-mass system

M. Pellicer¹ and
J. Solà-Morales^2,

1.
Dpt. d’Informàtica i Matemàtica Aplicada, Universitat de Girona, Campus Montilivi, Edif. P-IV, 17071 Girona
2.
Dpt. Matemàtica Aplicada 1, Universitat Politècnica de Catalunya, Avda. Diagonal, 647, 08028 Barcelona

Received: May 31, 2007

Revised: September 30, 2007

Published: April 2008

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Abstract

We consider a model for a damped spring-mass system that is a strongly damped wave equation with dynamic boundary conditions. In a previous paper we showed that for some values of the parameters of the model, the large time behaviour of the solutions is the same as for a classical spring-mass damper ODE. Here we use spectral analysis to show that for other values of the parameters, still of physical relevance and related to the effect of the spring inner viscosity, the limit behaviours are very different from that classical ODE.

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Mathematics Subject Classification: 35P05, 35B40.

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