Bounded solutions for non-autonomous parabolic equations

DOI10.1080/02681119608806219zbMath0857.34065OpenAlexW2024634139MaRDI QIDQ4887010

I. N. Stewart, Wei Nian Zhang

Publication date: 17 March 1997

Published in: Dynamics and Stability of Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/02681119608806219

zbMATH Keywords

functional differential equationsinfinite dimensionsexistence of bounded solutionsnon-autonomous perturbed parabolic partial differential equation

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Nonlinear differential equations in abstract spaces (34G20) Initial value problems for linear higher-order PDEs (35G10) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Higher-order parabolic equations (35K25)

Related Items (13)

Maximal attractors for the \(m\)-dimensional Cahn-Hilliard system ⋮ Admissibility and roughness of nonuniform exponential dichotomies for difference equations ⋮ Global bifurcations of a simply supported rectangular metallic plate subjected to a transverse harmonic excitation ⋮ The existences of transverse homoclinic solutions and chaos for parabolic equations ⋮ A BRIEF SURVEY ON CONSTRUCTING HOMOCLINIC STRUCTURES OF SOLITON EQUATIONS ⋮ Admissibility and nonuniform exponential dichotomies for difference equations without bounded growth or Lyapunov norms ⋮ Persistence of bounded solutions to degenerate Sobolev-Galpern equations ⋮ Persistence of bounded solutions of parabolic equations under domain perturbation ⋮ Computation of bifurcation manifolds of linearly independent homoclinic orbits ⋮ Unnamed Item ⋮ Linearly independent homoclinic bifurcations parameterized by a small function ⋮ Transversal homoclinic orbits and chaos for partial functional differential equations ⋮ Invariant foliations for parabolic equations

Cites Work

• Unnamed Item
• Exponential dichotomies, heteroclinic orbits, and Melnikov functions
• Exponential dichotomies and homoclinic orbits in functional differential equations
• Heteroclinic orbits for retarded functional differential equations
• An example of bifurcation to homoclinic orbits
• Bifurcation of degenerate homoclinics
• A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam
• Exponential dichotomies and transversal homoclinic points
• The Fredholm alternative and exponential dichotomies for parabolic equation
• Using Melnikov's method to solve Silnikov's problems
• Back in the Saddle Again: A Computer Assisted Study of the Kuramoto–Sivashinsky Equation
• The Existence of Homoclinic Orbits and the Method of Melnikov for Systems in $R^n$
• Transverse homoclinic orbits in periodically perturbed parabolic equations
• Bifurcation from a homoclinic orbit in parabolic differential equations

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