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.
On convergence to equilibrium for one-dimensional chain of harmonic oscillators in the half-line
Infinite Chain of Harmonic Oscillators Under the Action of the Stationary Stochastic Force
Large-time asymptotic behavior of the infinite system of harmonic oscillators
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