Strict Lyapunov functions and energy decay in Hamiltonian chains with degenerate damping
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929402591313920 |
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| author | Dymov, Andrey Lokutsievskiy, Lev Sarychev, Andrey |
| author_facet | Dymov, Andrey Lokutsievskiy, Lev Sarychev, Andrey |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19499 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strict Lyapunov functions and energy decay in Hamiltonian chains with degenerate damping Dymov, Andrey Lokutsievskiy, Lev Sarychev, Andrey Dynamical Systems Mathematical Physics Classical Analysis and ODEs 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. |
| title | Strict Lyapunov functions and energy decay in Hamiltonian chains with degenerate damping |
| topic | Dynamical Systems Mathematical Physics Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2406.19499 |