Local Attractors in a Certain Boundary-Value Problem for the Kuramoto–Sivashinsky Equation
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DOI: 10.1007/s10958-020-04883-1
Abstract: A boundary-value problem for the generalized Kuramoto–Sivashinsky equation with homogeneous Neumann boundary conditions is considered. The stability of spatially homogeneous equilibrium states are analyzed and local bifurcations at change of stability are studied. We use… read more here.
Keywords: value problem; kuramoto sivashinsky; boundary value; sivashinsky equation ... See more keywords
Stabilization of the linear Kuramoto-Sivashinsky equation with a delayed boundary control
Sign Up to like & getrecommendations! Published in 2019 at "IFAC-PapersOnLine"
DOI: 10.1016/j.ifacol.2019.08.013
Abstract: Abstract In this paper we stabilize the linear Kuramoto-Sivashinsky equation by means of a delayed boundary control. From the spectral decomposition of the spatial operator associated to the equation, we find that there is a… read more here.
Keywords: boundary control; sivashinsky equation; kuramoto sivashinsky; linear kuramoto ... See more keywords
Controlling roughening processes in the stochastic Kuramoto-Sivashinsky equation
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DOI: 10.1016/j.physd.2017.02.011
Abstract: We present a novel control methodology to control the roughening processes of semilinear parabolic stochastic partial differential equations in one dimension, which we exemplify with the stochastic Kuramoto-Sivashinsky equation. The original equation is split into… read more here.
Keywords: kuramoto sivashinsky; sivashinsky equation; control; roughening processes ... See more keywords
Lyapunov exponents of the Kuramoto--Sivashinsky PDE
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DOI: 10.21914/anziamj.v61i0.13939
Abstract: The Kuramoto–Sivashinsky equation is a prototypical chaotic nonlinear partial differential equation (PDE) in which the size of the spatial domain plays the role of a bifurcation parameter. We investigate the changing dynamics of the Kuramoto–Sivashinsky… read more here.
Keywords: pde; exponents kuramoto; kuramoto sivashinsky; sivashinsky pde ... See more keywords
Modified Kudryashov Method to Solve Generalized Kuramoto-Sivashinsky Equation
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DOI: 10.3390/sym10100527
Abstract: The generalized Kuramoto–Sivashinsky equation is investigated using the modified Kudryashov method for the new exact solutions. The modified Kudryashov method converts the given nonlinear partial differential equation to algebraic equations, as a result of various… read more here.
Keywords: kuramoto sivashinsky; kudryashov method; sivashinsky equation; modified kudryashov ... See more keywords
Asymptotic Distributions for Power Variations of the Solutions to Linearized Kuramoto-Sivashinsky SPDEs in One-to-Three Dimensions
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DOI: 10.3390/sym13010073
Abstract: We study the realized power variations for the fourth order linearized Kuramoto–Sivashinsky (LKS) SPDEs and their gradient, driven by the space–time white noise in one-to-three dimensional spaces, in time, have infinite quadratic variation and dimension-dependent… read more here.
Keywords: linearized kuramoto; kuramoto sivashinsky; lks spdes; one three ... See more keywords
Fractional View Analysis of Kuramoto-Sivashinsky Equations with Non-Singular Kernel Operators
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DOI: 10.3390/sym14071463
Abstract: In this article, we investigate the nonlinear model describing the various physical and chemical phenomena named the Kuramoto–Sivashinsky equation. We implemented the natural decomposition method, a novel technique, mixed with the Caputo–Fabrizio (CF) and Atangana–Baleanu… read more here.
Keywords: kuramoto sivashinsky; fractional view; proposed method; view analysis ... See more keywords
Global exact controllability to the trajectories of the Kuramoto-Sivashinsky equation
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DOI: 10.3934/eect.2020002
Abstract: In this paper, we establish the global exact controllability to the trajectories of the Kuramoto-Sivashinsky equation by five controls: one control is the right member of the equation and is constant with respect to the… read more here.
Keywords: exact controllability; kuramoto sivashinsky; global exact; trajectories kuramoto ... See more keywords