التفاصيل البيبلوغرافية
| العنوان: |
The damped Fermi–Pasta–Ulam oscillator |
| المؤلفون: |
László Hatvani |
| المصدر: |
Electronic Journal of Qualitative Theory of Differential Equations, Vol 2019, Iss 61, Pp 1-11 (2019) |
| بيانات النشر: |
University of Szeged, 2019. |
| سنة النشر: |
2019 |
| المجموعة: |
LCC:Mathematics |
| مصطلحات موضوعية: |
asymptotic stability, asymptotic stop, invariance principle, total mechanical energy, Mathematics, QA1-939 |
| الوصف: |
The system \begin{equation*} \ddot{q}_k+\gamma \dot{q}_k=V'(q_{k+1}-q_k)-V'(q_k-q_{k-1})\qquad (k=1,\ldots,N-2) \end{equation*} is considered, where $00$ (fixed endpoints – this is the original Fermi–Pasta–Ulam oscillator provided that the damping coefficient $\gamma$ equals zero); $q_1(t)-q_0(t)= L/(N-1)$, $q_{N-1}(t)-q_{N-2}(t)= L/(N-1)$ (free endpoints); $q_0(t)=-(K-q_{N-2}(t))$, $q_{N-1}(t)=q_1(t)+K$, $K=\hbox{const.}$ (cycle). We prove that the unique equilibrium state of the system with fixed endpoints is asymptotically stable. We also prove that the system with free endpoints and the cycle asymptotically stop at an equilibrium state along their arbitrary motion, i.e., for every motion there is $q_1^\infty\in\mathbb{R}$ such that $\lim_{t\to\infty}q_k(t)=q_1^\infty+(k-1)\overline{r}$, $\lim_{t\to\infty}\dot q_k(t)=0$ $(k=1,\ldots,N-2)$, where the constant $\overline{r}$ is defined by the equation $V'(\overline{r})=0$. |
| نوع الوثيقة: |
article |
| وصف الملف: |
electronic resource |
| اللغة: |
English |
| تدمد: |
1417-3875 |
| Relation: |
http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7610; https://doaj.org/toc/1417-3875 |
| DOI: |
10.14232/ejqtde.2019.1.61 |
| URL الوصول: |
https://doaj.org/article/8797096f8a5f45f1b1b261562f5c77a5 |
| رقم الانضمام: |
edsdoj.8797096f8a5f45f1b1b261562f5c77a5 |
| قاعدة البيانات: |
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