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Stabilization of Statistical Solutions for an Infinite Inhomogeneous Chain of Harmonic Oscillators

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Abstract

An infinite inhomogeneous harmonic chain of particles with different force constants of interaction is considered. The large time behavior of distributions of the solutions to the Cauchy problem with random initial data is studied. The main result of the paper establishes the convergence of these distributions to a limiting measure.

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Funding

This work is supported by the Russian Science Foundation under grant 19-71-30004).

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Authors and Affiliations

  1. Keldysh Institute of AppliedMathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia

    T. V. Dudnikova

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  1. T. V. Dudnikova
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Correspondence to T. V. Dudnikova.

Additional information

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Vol. 308, pp. 181–196.

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Dudnikova, T.V. Stabilization of Statistical Solutions for an Infinite Inhomogeneous Chain of Harmonic Oscillators. Proc. Steklov Inst. Math. 308, 168–183 (2020). https://doi.org/10.1134/S0081543820010137

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  • DOI: https://doi.org/10.1134/S0081543820010137

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