Finite mechanical proxies for a class of reducible continuum systems

Franco Cardin; Alberto Lovison; Franco Cardin; Alberto Lovison

doi:10.3934/nhm.2014.9.417

Networks and Heterogeneous Media

2014, Volume 9, Issue 3: 417-432. doi: 10.3934/nhm.2014.9.417

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Finite mechanical proxies for a class of reducible continuum systems

Franco Cardin ^{1
,},
Alberto Lovison ^{1
,}

1.
Dipartimento di Matematica, Università degli Studi di Padova, Via Trieste, 63 - 35121 Padova

Received: 01 June 2013 Revised: 01 May 2014
Primary: 74B20, 70J50; Secondary: 65F18.

We present the exact finite reduction of a class of nonlinearly perturbed wave equations --typically, a non-linear elastic string-- based on the Amann--Conley--Zehnder paradigm. By solving an inverse eigenvalue problem, we establish an equivalence between the spectral finite description derived from A--C--Z and a discrete mechanical model, a well definite finite spring--mass system. By doing so, we decrypt the abstract information encoded in the finite reduction and obtain a physically sound proxy for the continuous problem.
- Nonlinear wave equation,
- exact finite reductions,
- thermodynamical limit,
- collective variables,
- inverse eigenvalue problems
Citation: Franco Cardin, Alberto Lovison. Finite mechanical proxies for a class of reducible continuum systems[J]. Networks and Heterogeneous Media, 2014, 9(3): 417-432. doi: 10.3934/nhm.2014.9.417

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Abstract

We present the exact finite reduction of a class of nonlinearly perturbed wave equations --typically, a non-linear elastic string-- based on the Amann--Conley--Zehnder paradigm. By solving an inverse eigenvalue problem, we establish an equivalence between the spectral finite description derived from A--C--Z and a discrete mechanical model, a well definite finite spring--mass system. By doing so, we decrypt the abstract information encoded in the finite reduction and obtain a physically sound proxy for the continuous problem.

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