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Finite mechanical proxies for a class of reducible continuum systems

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  • 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.
    Mathematics Subject Classification: Primary: 74B20, 70J50; Secondary: 65F18.

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