Erratum to: Asymptotic estimates and stability analysis of Kuramoto-Sivashinsky type models
نویسندگان
چکیده
منابع مشابه
Asymptotic estimates and stability analysis of Kuramoto-Sivashinsky type models
We first show asymptotic L bounds for a class of equations, which includes the Burger-Sivashinsly model for odd solutions with periodic boundary conditions. We consider the conditional stability of stationary solutions of Kuramoto-Sivashinsky equation in the periodic setting. We establish rigorously the general structure of the spectrum of the linearized operator. In addition, we show condition...
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In this note, we announce a general result resolving the long-standing question of nonlinear modulational stability, or stability with respect to localized perturbations, of periodic travelingwave solutions of the generalized Kuramoto–Sivashinski equation, establishing that spectral modulational stability, defined in the standard way, implies nonlinear modulational stability with sharp rates of...
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We consider the Kuramoto-Sivashinsky (KS) equation in one dimension with periodic boundary conditions. We apply a Lyapunov function argument similar to the one first introduced by Nicolaenko, Scheurer, and Temam [18], and later improved by Collet, Eckmann, Epstein and Stubbe[1], and Goodman [10] to prove that lim sup t→∞ ||u||2 ≤ CL 3 2 . This result is slightly weaker than that recently announ...
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A model consisting of a mixed Kuramoto-Sivashinsky-Kortewegde Vries equation, linearly coupled to an extra linear dissipative equation has been proposed in [1] in order to describe the surface waves on multi-layered liquid films and stability criteria are discussed using wave mode analysis. In this paper, we study the linear stability of solutions to the model from the viewpoint of energy estim...
متن کاملAsymptotic synchronous behavior of Kuramoto type models with frustrations
We present a quantitative asymptotic behavior of coupled Kuramoto oscillators with frustrations and give some sufficient conditions for the parameters and initial condition leading to phase or frequency synchronization. We consider three ensembles of Kuramoto oscillators with frustration. First, we study a general case with nonidentical oscillators; i.e., the natural frequencies are distributed...
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ژورنال
عنوان ژورنال: Journal of Evolution Equations
سال: 2011
ISSN: 1424-3199,1424-3202
DOI: 10.1007/s00028-011-0118-y