Self-excited vibrations for damped and delayed 1-dimensional wave equations

DOI10.1007/s10884-018-9654-2zbMath1421.35021OpenAlexW2793453534MaRDI QIDQ1739076

Nemanja Kosovalić, Brian Pigott

Publication date: 25 April 2019

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-018-9654-2

zbMATH Keywords

Hopf bifurcationLyapunov-Schmidt methodsine-Gordon equationimplicit function theoremFourier expansionssmall divisorsderivative loss property

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Periodic solutions to PDEs (35B10) Bifurcations in context of PDEs (35B32) Second-order semilinear hyperbolic equations (35L71)

Related Items (7)

Symmetric vibrations of higher dimensional nonlinear wave equations ⋮ Hopf bifurcation for general 1D semilinear wave equations with delay ⋮ Persistence and smooth dependence on parameters of periodic orbits in functional differential equations close to an ODE or an evolutionary PDE ⋮ Regularity of time-periodic solutions to autonomous semilinear hyperbolic PDEs ⋮ Quasi‐periodic traveling waves for a class of damped beams on rectangular tori ⋮ Self-excited vibrations for damped and delayed higher dimensional wave equations ⋮ Quasi-periodic travelling waves for beam equations with damping on 3-dimensional rectangular tori

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