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2008, 7(3): 563-577. doi: 10.3934/cpaa.2008.7.563

Spectral analysis and limit behaviours in a spring-mass system

1. 

Dpt. d’Informàtica i Matemàtica Aplicada, Universitat de Girona, Campus Montilivi, Edif. P-IV, 17071 Girona, Spain

2. 

Dpt. Matemàtica Aplicada 1, Universitat Politècnica de Catalunya, Avda. Diagonal, 647, 08028 Barcelona, Spain

Received  June 2007 Revised  October 2007 Published  February 2008

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.
Citation: M. Pellicer, J. Solà-Morales. Spectral analysis and limit behaviours in a spring-mass system. Communications on Pure & Applied Analysis, 2008, 7 (3) : 563-577. doi: 10.3934/cpaa.2008.7.563
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