Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle

DOI10.1016/j.jde.2003.10.027zbMath1064.35076OpenAlexW2060613029WikidataQ60143396 ScholiaQ60143396MaRDI QIDQ1880772

Bernold Fiedler, Carlos Rocha, Matthias Wolfrum

Publication date: 1 October 2004

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

Full work available at URL: https://doi.org/10.1016/j.jde.2003.10.027

zbMATH Keywords

one space dimensionreaction-advection-diffusion equationscomplete combinatorial description of the attractorzero number properties

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (18)

Schoenflies spheres as boundaries of bounded unstable manifolds in gradient Sturm systems ⋮ A symmetry property for fully nonlinear elliptic equations on the sphere ⋮ Static large deviations for a reaction-diffusion model ⋮ Sturm attractors for fully nonlinear parabolic equations ⋮ Generic Morse-Smale property for the parabolic equation on the circle ⋮ Scalar autonomous second order ordinary differential equations ⋮ A permutation characterization of Sturm global attractors of Hamiltonian type ⋮ Transversality in scalar reaction-diffusion equations on a circle ⋮ Spectrum and amplitude equations for scalar delay-differential equations with large delay ⋮ Symmetry and bifurcation of periodic solutions in Neumann boundary value problems ⋮ Realization of period maps of planar Hamiltonian systems ⋮ Connectivity and design of planar global attractors of Sturm type. II: Connection graphs ⋮ 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 ⋮ Scalar parabolic PDEs and braids ⋮ Slowly non-dissipative equations with oscillating growth ⋮ Unbounded Sturm Global Attractors for Semilinear Parabolic Equations on the Circle

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