Infinite non homogeneous chain of harmonic oscillators: Stabilization of statistical solutions

T. V. Dudnikova


Abstract: An infinite irregular harmonic chain of particles is considered. We assume that a single particle (“defect”) in the chain has a mass different from the mass of the other particles. For large times we study the behavior of distributions of solutions of the Cauchy problem with random initial conditions. The main goal is to prove the convergence of these distributions to a limiting measure.

Keywords: infinite chain of harmonic oscillators with a defect, Cauchy problem, random initial data, weak convergence of measures.

DOI: 10.20948/prepr-2018-254

Bibliographic databases:

•