Energy Decay of Damped Systems

2003/12/19 by Krešimir Veselić, Veselić, Krešimir
Computer Science · Mathematics · Physics and Astronomy · #47D06 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math/0312376

openalex publication_date 2003/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a new and simple bound for the exponential decay of second order systems using the spectral shift. This result is applied to finite matrices as well as to partial differential equations of Mathematical Physics. The type of the generated semigroup is shown to be bounded by the upper real part of the numerical range of the underlying quadratic operator pencil.

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