Generalized Korteweg-de Vries equation in \(H^1(\mathbb R)\)

DOI10.1016/j.na.2009.02.062zbMath1167.35464OpenAlexW2285198875MaRDI QIDQ1029431

Tomasz Dlotko, Maria B. Kania, Mei-Hua Yang

Publication date: 10 July 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.02.062

zbMATH Keywords

global solvabilitygeneralized KdV equationglobal attractor in \(H^1(\mathbb R)\)

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Attractors (35B41) KdV equations (Korteweg-de Vries equations) (35Q53)

Related Items (9)

Higher regularity of global attractors of a weakly dissipative fractional Korteweg de Vries equation ⋮ The generalized Korteweg-de Vries-Burgers equation in \(H^2(\mathbb R)\) ⋮ Long time behavior of solutions of gKdV equations ⋮ Asymptotic behavior of the generalized Korteweg-de Vries-Burgers equation ⋮ Navier-Stokes equation and its fractional approximations ⋮ Pullback attractors for generalized Korteweg-de Vries-Burgers equations ⋮ GLOBAL ATTRACTOR FOR WEAKLY DAMPED, FORCED mKdV EQUATION BELOW ENERGY SPACE ⋮ Global attractor for the periodic generalized Korteweg-de Vries equation through smoothing ⋮ Global attractor for weakly damped, forced mKdV equation in low regularity spaces

Cites Work

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• Semigroups of linear operators and applications to partial differential equations
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• Infinite-dimensional dynamical systems in mechanics and physics.
• Asymptotic smoothing and the global attractor of a weakly damped KdV equation on the real line.
• Chaos for a damped and forced KdV equation
• Well-Posedness of the Initial Value Problem for the Korteweg-de Vries Equation
• Attractors for non-compact semigroups via energy equations
• Well‐posedness and scattering results for the generalized korteweg‐de vries equation via the contraction principle

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