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Local Attractors in a Certain Boundary-Value Problem for the Kuramoto–Sivashinsky Equation

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0 Published in 2020 at "Journal of Mathematical Sciences"

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

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0 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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0 Published in 2017 at "Physica D: Nonlinear Phenomena"

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

High Accuracy Analysis of Nonconforming Mixed Finite Element Method for the Nonlinear Sivashinsky Equation

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0 Published in 2020 at "Mathematical Problems in Engineering"

DOI: 10.1155/2020/8416898

Abstract: The fourth-order nonlinear Sivashinsky equation is often used to simulate a planar solid-liquid interface for a binary alloy. In this paper, we study the high accuracy analysis of the nonconforming mixed finite element method (MFEM… read more here.

Keywords: sivashinsky equation; analysis; method; nonlinear sivashinsky ... See more keywords

Modified Kudryashov Method to Solve Generalized Kuramoto-Sivashinsky Equation

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0 Published in 2018 at "Symmetry"

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