Generic hyperbolicity of equilibria and periodic orbits of the parabolic equation on the circle

DOI10.1090/S0002-9947-2010-04890-1zbMath1205.35151arXiv0806.2713MaRDI QIDQ3053470

Romain Joly, Geneviève Raugel

Publication date: 29 October 2010

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0806.2713

zbMATH Keywords

lap numberSard-Smale theorem

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Periodic solutions to PDEs (35B10) Reaction-diffusion equations (35K57) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Dynamical systems with hyperbolic orbits and sets (37D05) Hyperbolicity, Lyapunov functions for infinite-dimensional dissipative dynamical systems (37L45) Morse-Smale systems (37D15) Semilinear parabolic equations (35K58)

Related Items (14)

Long-time behavior of almost periodically forced parabolic equations on the circle ⋮ A class of generically Morse-Smale monotone, dynamical systems ⋮ Almost automorphically-forced flows on \(S^1\) or \(\mathbb{R}\) in one-dimensional almost periodic semilinear heat equations ⋮ Transversality for cyclic negative feedback systems ⋮ Generic Morse-Smale property for the parabolic equation on the circle ⋮ Almost automorphically and almost periodically forced circle flows of almost periodic parabolic equations on \(S^1\) ⋮ A permutation characterization of Sturm global attractors of Hamiltonian type ⋮ Global Sign-changing Solutions of a Higher Order Semilinear Heat Equation in the Subcritical Fujita Range ⋮ Classification of Global and Blow-up Sign-changing Solutions of a Semilinear Heat Equation in the Subcritical Fujita Range : Second-order Diffusion ⋮ On a definition of Morse-Smale evolution processes ⋮ Non-wandering points for autonomous/periodic parabolic equations on the circle ⋮ Unbounded Sturm Global Attractors for Semilinear Parabolic Equations on the Circle ⋮ In memoriam: Geneviève Raugel ⋮ Generic transversality of heteroclinic and homoclinic orbits for scalar parabolic equations

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