Hopf bifurcation for general 1D semilinear wave equations with delay

DOI10.1007/s10884-021-10009-1zbMath1491.35012arXiv2011.06824OpenAlexW3167227628WikidataQ115383168 ScholiaQ115383168MaRDI QIDQ2134144

Lutz Recke, I. Ya. Kmit'

Publication date: 6 May 2022

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

Full work available at URL: https://arxiv.org/abs/2011.06824

zbMATH Keywords

dissipationLyapunov-Schmidt reductiontime-periodic solutions

Mathematics Subject Classification ID

Initial-boundary value problems for second-order hyperbolic equations (35L20) Periodic solutions to PDEs (35B10) Partial functional-differential equations (35R10) Bifurcations in context of PDEs (35B32) Second-order semilinear hyperbolic equations (35L71)

Cites Work

• Unnamed Item
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• Small divisor problems in fluid mechanics
• Local existence, uniqueness and smooth dependence for nonsmooth quasilinear parabolic problems
• Finding periodic orbits in state-dependent delay differential equations as roots of algebraic equations
• Solution regularity and smooth dependence for abstract equations and applications to hyperbolic PDEs
• Hopf bifurcation for non-densely defined Cauchy problems
• Local bifurcations, center manifolds, and normal forms in infinite-dimensional dynamical systems
• Boundary layer solutions to problems with infinite-dimensional singular and regular perturbations
• A modified Poincaré method for the persistence of periodic orbits and applications
• On the spectrum of evolution operators generated by hyperbolic systems
• The Hopf bifurcation theorem in infinite dimensions
• Stability and stabilization of infinite dimensional systems with applications
• Introduction to functional differential equations
• Bifurcation theory. An introduction with applications of PDEs
• An algorithm for Hopf bifurcation analysis of a delayed reaction-diffusion model
• Self-excited vibrations for damped and delayed higher dimensional wave equations
• Self-excited vibrations for damped and delayed 1-dimensional wave equations
• Periodic solutions to nonlinear wave equation with \(X\)-dependent coefficients under the general boundary conditions
• On the linear stability of hyperbolic PDEs and viscoelastic flows
• Theory and applications of partial functional differential equations
• Bifurcation theory of functional differential equations
• Theory and applications of abstract semilinear Cauchy problems
• Bifurcation analysis for a delayed diffusive logistic population model in the advective heterogeneous environment
• Double Hopf bifurcation in delayed reaction-diffusion systems
• Hopf bifurcation for semilinear dissipative hyperbolic systems
• Generic transversality property for a class of wave equations with variable damping
• Time-periodic Second-order Hyperbolic Equations: Fredholmness, Regularity, and Smooth Dependence
• Spectral mapping theorem for linear hyperbolic systems
• Center manifolds for semilinear equations with non-dense domain and applications to Hopf bifurcation in age structured models
• The G-invariant implicit function theorem in infinite dimensions
• Persistence of Periodic Orbits for Perturbed Dissipative Dynamical Systems
• Normal forms and Hopf bifurcation for partial differential equations with delays
• Bifurcation analysis of coexistent state in a delayed two-species predator-prey model
• Hopf Bifurcation for Semilinear FDEs in General Banach Spaces
• Control of Wave and Beam PDEs
• Applied Delay Differential Equations
• The implicit function theorem and multi-bump solutions of periodic partial differential equations
• SMALL DENOMINATORS AND PROBLEMS OF STABILITY OF MOTION IN CLASSICAL AND CELESTIAL MECHANICS