A modified Poincaré method for the persistence of periodic orbits and applications

DOI10.1007/s10884-009-9155-4zbMath1189.35018OpenAlexW2074752818MaRDI QIDQ970548

Geneviève Raugel, Jack K. Hale

Publication date: 19 May 2010

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

Full work available at URL: https://doi.org/10.1007/s10884-009-9155-4

zbMATH Keywords

Lyapunov-Schmidt methoddamped wave equationsPoincaré methodsecond grade fluid equationsasymptotically smooth systemsperturbed Navier-Stokes equations

Mathematics Subject Classification ID

Abstract parabolic equations (35K90) PDEs in connection with fluid mechanics (35Q35) Periodic solutions to PDEs (35B10) Singular perturbations in context of PDEs (35B25) Navier-Stokes equations (35Q30) General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations (37L05) Abstract hyperbolic equations (35L90) Noncompact semigroups, dispersive equations, perturbations of infinite-dimensional dissipative dynamical systems (37L50)

Related Items

Hopf bifurcation for general 1D semilinear wave equations with delay, Topological structural stability of partial differential equations on projected spaces, Persistence and smooth dependence on parameters of periodic orbits in functional differential equations close to an ODE or an evolutionary PDE, Hopf bifurcation for semilinear dissipative hyperbolic systems, Solution regularity and smooth dependence for abstract equations and applications to hyperbolic PDEs, Obituary of Jack K. Hale, Fredholm operators, evolution semigroups, and periodic solutions of nonlinear periodic systems, Regularity of the global attractor and finite-dimensional behavior for the second grade fluid equations, In memoriam: Geneviève Raugel, Generic transversality of heteroclinic and homoclinic orbits for scalar parabolic equations

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