Behavior for large time of an infinite chain of harmonic oscillators with defects

2019/09/15 by T. V. Dudnikova, Dudnikova, T. V.
Computer Science · Engineering · Mathematics · #35B40 #35L15 #35Q70 #70F45 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #FOS: Physical sciences #Mathematical Physics (math-ph) #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1909.06764

openalex publication_date 2019/09/15 · openalex created_date 2019/09/19 · openalex updated_date 2026/07/28

Abstract

An infinite irregular harmonic chain of particles is considered. We assume that some particles (``defects'') in the chain have masses and force constants of interaction different from the masses and the interaction constants of the other particles. We study the Cauchy problem for this model. The main goal is to study the long-time behavior and derive the dispersive bounds for the solutions in the energy weighted norms.

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