کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5774073 | 1413543 | 2017 | 45 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the global well-posedness of BV weak solutions to the Kuramoto-Sakaguchi equation
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
آنالیز ریاضی
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
The Kuramoto model is a prototype phase model describing the synchronous behavior of weakly coupled limit-cycle oscillators. When the number of oscillators is sufficiently large, the dynamics of Kuramoto ensemble can be effectively approximated by the corresponding mean-field equation, namely “the Kuramoto-Sakaguchi (KS) equation”. This KS equation is a kind of scalar conservation law with a nonlocal flux function due to the mean-field interactions among oscillators. In this paper, we provide a unique global solvability of bounded variation (BV) weak solutions to the kinetic KS equation for identical oscillators using the method of front-tracking in hyperbolic conservation laws. Moreover, we also show that our BV weak solutions satisfy local-in-time L1-stability with respect to BV-initial data. For the ensemble of identical Kuramoto oscillators, we explicitly construct an exponentially growing BV weak solution generated from BV perturbation of incoherent state for any positive coupling strength. This implies the nonlinear instability of incoherent state in a positive coupling strength regime. We provide several numerical examples and compare them with our analytical results.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Differential Equations - Volume 262, Issue 2, 15 January 2017, Pages 978-1022
Journal: Journal of Differential Equations - Volume 262, Issue 2, 15 January 2017, Pages 978-1022
نویسندگان
Debora Amadori, Seung-Yeal Ha, Jinyeong Park,