Recurrent Solutions of a Nonautonomous Modified Swift-Hohenberg Equation

Jintao Wang, Lu Yang and Jinqiao Duan

Applied Mathematics and Computation, 2020, vol. 379, issue C

Abstract: We consider recurrent solutions of the nonautonomous modified Swift-Hohenberg equationut+Δ2u+2Δu+au+b|∇u|2+u3=g(t,x).We employ Conley index theory to show that, if the forcing g:R→L2(Ω) is a recurrent function, then there are at least two recurrent solutions in H02(Ω) under appropriate assumptions on the parameters a, b and g.

Keywords: Modified Swift-Hohenberg equations; Nonautonomous dynamical systems; Recurrent functions; Conley index; Gradient systems (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:379:y:2020:i:c:s0096300320302393

DOI: 10.1016/j.amc.2020.125270

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