Transversality in scalar reaction-diffusion equations on a circle

DOI10.1016/j.jde.2008.01.018zbMath1157.35004OpenAlexW2145078062WikidataQ60143393 ScholiaQ60143393MaRDI QIDQ932842

Carlos Rocha, Radosław Czaja

Publication date: 11 July 2008

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

Full work available at URL: https://doi.org/10.1016/j.jde.2008.01.018

zbMATH Keywords

transversalityPeriodic orbithyperbolic periodic orbitMatano's zero number theoryno homoclinic connectionszero number

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Periodic solutions to PDEs (35B10) Reaction-diffusion equations (35K57)

Related Items (13)

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 ⋮ 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 ⋮ Generic hyperbolicity of equilibria and periodic orbits of the parabolic equation on the circle ⋮ Non-wandering points for autonomous/periodic parabolic equations on the circle ⋮ Unbounded Sturm Global Attractors for Semilinear Parabolic Equations on the Circle ⋮ Generic transversality of heteroclinic and homoclinic orbits for scalar parabolic equations

Cites Work

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• Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle
• Jacobi matrices and transversality
• A stability theorem for solutions of abstract differential equations, and its application to the study of the local behavior of solutions of elliptic equations
• The Dynamics of Rotating Waves in Scalar Reaction Diffusion Equations
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• Invariant foliations near normally hyperbolic invariant manifolds for semiflows
• Sur l'unicité réctrograde dans les problèmes mixtes paraboliques.
• Analytic semigroups and optimal regularity in parabolic problems
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