Periodic limit for non-autonomous Lagrangian systems and applications to a Kuramoto type model
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908602763051008 |
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| author | Danesi, Veronica Mendico, Cristian Tao, Xuan Wang, Kaizhi |
| author_facet | Danesi, Veronica Mendico, Cristian Tao, Xuan Wang, Kaizhi |
| contents | This paper explores the asymptotic properties of non-autonomous Lagrangian systems, assuming that the associated Tonelli Lagrangian converges to a time-periodic function. Specifically, given a continuous initial condition, we provide a suitable construction of a Lax-Oleinik semigroup such that it converges toward a periodic solution of the equation. Moreover, the graph of its gradient converges as time tends to infinity to the graph of the gradient of the periodic limit function with respect to the Hausdorff distance. Finally, we apply this result to a Kuramoto-type model, proving the existence of an invariant torus given by the graph of the gradient of the limiting periodic solution of the Hamilton-Jacobi equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_17242 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Periodic limit for non-autonomous Lagrangian systems and applications to a Kuramoto type model Danesi, Veronica Mendico, Cristian Tao, Xuan Wang, Kaizhi Optimization and Control Mathematical Physics Analysis of PDEs This paper explores the asymptotic properties of non-autonomous Lagrangian systems, assuming that the associated Tonelli Lagrangian converges to a time-periodic function. Specifically, given a continuous initial condition, we provide a suitable construction of a Lax-Oleinik semigroup such that it converges toward a periodic solution of the equation. Moreover, the graph of its gradient converges as time tends to infinity to the graph of the gradient of the periodic limit function with respect to the Hausdorff distance. Finally, we apply this result to a Kuramoto-type model, proving the existence of an invariant torus given by the graph of the gradient of the limiting periodic solution of the Hamilton-Jacobi equation. |
| title | Periodic limit for non-autonomous Lagrangian systems and applications to a Kuramoto type model |
| topic | Optimization and Control Mathematical Physics Analysis of PDEs |
| url | https://arxiv.org/abs/2510.17242 |