Work

Strict Lyapunov Functions and Energy Decay in Hamiltonian Chains with Degenerate Damping

Year: 2024

Type: article

Abstract: We consider a Hamiltonian chain of rotators (in general nonlinear) in which the first rotator is damped. Being motivated by problems of nonequilibrium statistical mechanics of crystals, we construct a strict Lyapunov function that allows us to find a lower bound for the total energy dissipation rate when the energy and time are large. Our construction is explicit and its analysis is rather straightforward. We rely on a method going back to Matrosov, Malisoff, and Mazenc, which we review in our paper. The method is rather universal, and we show that it is applicable to a chain of oscillators as well.

Source: Proceedings of the Steklov Institute of Mathematics

DOI: 10.1134/s0081543824060075

Authors: Andrey V. Dymov, Lev V. Lokutsievskiy, Andrey V. Sarychev

Institutions: National Research University Higher School of Economics, Steklov Mathematical Institute, University of Florence

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funder: Russian Science Foundation

Award: G5112716591