Poincaré–Bendixson theory for certain reaction–diffusion boundary-value problems

DOI10.1017/S0308210500029188zbMath0796.35075MaRDI QIDQ4294343

Russell A. Smith

Publication date: 25 September 1994

Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)

zbMATH Keywords

Hausdorff dimensioncompact invariant setanlogue of the Poincaré-Bendixson theory

Mathematics Subject Classification ID

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Reaction-diffusion equations (35K57)

Related Items (2)

Unnamed Item ⋮ Frequency theorem for parabolic equations and its relation to inertial manifolds theory

Cites Work

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• A Poincaré-Bendixson theorem for scalar reaction diffusion equations
• Large diffusivity and asymptotic behavior in parabolic systems
• Massera's convergence theorem for periodic nonlinear differential equations
• Geometric theory of semilinear parabolic equations
• Infinite-dimensional dynamical systems in mechanics and physics
• An application of the invariance principle to reaction diffusion equations
• Attractors for reaction-diffusion equations: existence and estimate of their dimension
• Convergence Theorems for Periodic Retarded Functional Differential Equations
• A bifurcation problem for a nonlinear partial differential equation of parabolic type^†
• Large Time Behavior of Solutions of Systems of Nonlinear Reaction-Diffusion Equations

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