Dynamics of periodically forced parabolic equations on the circle

DOI10.1017/S0143385700006933zbMath0754.35066OpenAlexW2127259639MaRDI QIDQ4015523

Björn Sandstede, Bernold Fiedler

Publication date: 18 January 1993

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385700006933

zbMATH Keywords

large time behaviour of solutions of nonautonomous equations

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Dynamics induced by flows and semiflows (37C10)

Related Items (19)

Generic behavior of flows strongly monotone with respect to high-rank cones ⋮ Heteroclinic orbits between rotating waves of semilinear parabolic equations on the circle ⋮ Long-time behavior of almost periodically forced parabolic equations on the circle ⋮ Structure of \(\omega\)-limit sets for almost-periodic parabolic equations on \(S^{1}\) with reflection symmetry ⋮ Almost automorphically-forced flows on \(S^1\) or \(\mathbb{R}\) in one-dimensional almost periodic semilinear heat equations ⋮ Unnamed Item ⋮ Inverse problems and chaotic dynamics of parabolic equations on arbitrary spatial domains ⋮ 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 \(S^1\) ⋮ Transversality in scalar reaction-diffusion equations on a circle ⋮ Generic hyperbolicity of equilibria and periodic orbits of the parabolic equation on the circle ⋮ On Minimal Sets of Scalar Parabolic Equations with Skew-Product Structures ⋮ Non-wandering points for autonomous/periodic parabolic equations on the circle ⋮ Unnamed Item ⋮ Complicated dynamics of parabolic equations with simple gradient dependence ⋮ Existence of partially localized quasiperiodic solutions of homogeneous elliptic equations on R^{N+1} ⋮ The existence of partially localized periodic-quasiperiodic solutions and related KAM-type results for elliptic equations on the entire space ⋮ Ergodic attractors and almost-everywhere asymptotics of scalar semilinear parabolic differential equations ⋮ Asymptotic behavior of solutions of nonlinear parabolic equations on two-layer thin domains

Cites Work

• Unnamed Item
• Convergence, asymptotic periodicity, and finite-point blow-up in one- dimensional semilinear heat equations
• A Poincaré-Bendixson theorem for scalar reaction diffusion equations
• Geometric theory of semilinear parabolic equations
• The Dynamics of Rotating Waves in Scalar Reaction Diffusion Equations
• Convergence in general periodic parabolic equations in one space dimension

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