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

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.

• Publication year

  2024

• Venue

  Proceedings of the Steklov Institute of Mathematics

• Publication date

  2024-06-27

• Fields of study

  Mathematics, Physics

• Identifiers
  DOI 10.1134/S0081543824060075arXiv 2406.19499
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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