Positive Solutions for Nonlocal Extended Fisher–Kolmogorov and Swift–Hohenberg Equations
Sign Up to like & getrecommendations! Published in 2021 at "Mediterranean Journal of Mathematics"
DOI: 10.1007/s00009-021-01709-5
Abstract: In this paper we study the existence of positive solutions for a class of nonlocal fourth-order nonautonomous differential equations which can be seen as generalization of extended Fisher-Kolmogorov and Swift-Hohenberg equations. The main result is… read more here.
Keywords: fisher kolmogorov; swift hohenberg; extended fisher; positive solutions ... See more keywords
Analytical solution of non-linear fractional order Swift-Hohenberg equations
Sign Up to like & getrecommendations! Published in 2021 at "Ain Shams Engineering Journal"
DOI: 10.1016/j.asej.2020.11.019
Abstract: Abstract In this paper, we find approximate analytical solutions to fractional order “Swift-Hohenberg equations” by using Laplace Adomian decomposition method (LADM). With the help of the this method, we investigate various types of problems involving… read more here.
Keywords: swift hohenberg; order swift; order; fractional order ... See more keywords
Local control of globally competing patterns in coupled Swift-Hohenberg equations.
Sign Up to like & getrecommendations! Published in 2018 at "Chaos"
DOI: 10.1063/1.5018139
Abstract: We present analytical and numerical investigations of two anti-symmetrically coupled 1D Swift-Hohenberg equations (SHEs) with cubic nonlinearities. The SHE provides a generic formulation for pattern formation at a characteristic length scale. A linear stability analysis… read more here.
Keywords: different patterns; hohenberg equations; coupled swift; swift hohenberg ... See more keywords
Upper semi-continuity of random attractors and existence of invariant measures for nonlocal stochastic Swift–Hohenberg equation with multiplicative noise
Sign Up to like & getrecommendations! Published in 2021 at "Journal of Mathematical Physics"
DOI: 10.1063/5.0039187
Abstract: In this paper, we mainly study the long-time dynamical behaviors of 2D nonlocal stochastic Swift-Hohenberg equations with multiplicative noise from two perspectives. Firstly, by adopting the analytic semigroup theory, we prove the upper semi-continuity of… read more here.
Keywords: upper semi; semi continuity; swift hohenberg; multiplicative noise ... See more keywords
Final patterns and bifurcation analysis of the odd-periodic Swift–Hohenberg equation with respect to the period
Sign Up to like & getrecommendations! Published in 2019 at "Applicable Analysis"
DOI: 10.1080/00036811.2019.1659954
Abstract: ABSTRACT We study the bifurcation analysis of the Swift–Hohenberg equation (SHE) with the odd-periodic condition as period parameter λ moves. Motivated by Peletier and Rottschäfer [Pattern selection of solutions of the Swift–Hohenberg equations. Phys D.… read more here.
Keywords: bifurcation analysis; hohenberg equation; odd periodic; swift hohenberg ... See more keywords
Global martingale and pathwise solutions and infinite regularity of invariant measures for a stochastic modified Swift–Hohenberg equation
Sign Up to like & getrecommendations! Published in 2022 at "Nonlinearity"
DOI: 10.1088/1361-6544/acc6b1
Abstract: We consider a 2D stochastic modified Swift–Hohenberg equations with multiplicative noise and periodic boundary. First, we establish the existence of local and global martingale and pathwise solutions in the regular Sobolev space H2m for each… read more here.
Keywords: pathwise; invariant measures; modified swift; stochastic modified ... See more keywords
Defectlike structures and localized patterns in the cubic-quintic-septic Swift-Hohenberg equation.
Sign Up to like & getrecommendations! Published in 2019 at "Physical review. E"
DOI: 10.1103/physreve.100.012204
Abstract: We study numerically the cubic-quintic-septic Swift-Hohenberg (SH357) equation on bounded one-dimensional domains. Under appropriate conditions stripes with wave number k≈1 bifurcate supercritically from the zero state and form S-shaped branches resulting in bistability between small… read more here.
Keywords: septic swift; swift hohenberg; defectlike structures; cubic quintic ... See more keywords
Spatially extended dislocations produced by the dispersive Swift-Hohenberg equation.
Sign Up to like & getrecommendations! Published in 2022 at "Physical review. E"
DOI: 10.1103/physreve.107.044214
Abstract: Motivated by previous results showing that the addition of a linear dispersive term to the two-dimensional Kuramoto-Sivashinsky equation has a dramatic effect on the pattern formation, we study the Swift-Hohenberg equation with an added linear dispersive term,… read more here.
Keywords: equation; hohenberg equation; dispersive swift; swift hohenberg ... See more keywords
An Iterative Method for Time-Fractional Swift-Hohenberg Equation
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DOI: 10.1155/2018/2405432
Abstract: We study a type of iterative method and apply it to time-fractional Swift-Hohenberg equation with initial value. Using this iterative method, we obtain the approximate analytic solutions with numerical figures to initial value problems, which… read more here.
Keywords: iterative method; time fractional; swift hohenberg; fractional swift ... See more keywords
A Fast and Efficient Numerical Algorithm for the Nonlocal Conservative Swift–Hohenberg Equation
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DOI: 10.1155/2020/7012483
Abstract: In this paper, we consider a new Swift–Hohenberg equation, where the total mass of this model is conserved through a nonlocal Lagrange multiplier. Based on the operator splitting method and spectral method, a fast and… read more here.
Keywords: efficient numerical; hohenberg equation; fast efficient; swift hohenberg ... See more keywords
Averaging principles for the Swift-Hohenberg equation
Sign Up to like & getrecommendations! Published in 2020 at "Communications on Pure and Applied Analysis"
DOI: 10.3934/cpaa.2020016
Abstract: This work studies the effects of rapid oscillations (with respect to time) of the forcing term on the long-time behaviour of the solutions of the Swift-Hohenberg equation. More precisely, we establish three kinds of averaging… read more here.
Keywords: swift hohenberg; time; hohenberg equation; principles swift ... See more keywords