Compact invariant sets for some quasilinear nonlocal Kirchhoff strings on ℝN

DOI10.1080/00036810601127418zbMath1144.35355OpenAlexW2155016628WikidataQ58242471 ScholiaQ58242471MaRDI QIDQ5457911

Perikles G. Papadopoulos, Nikolaos M. Stavrakakis

Publication date: 10 April 2008

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036810601127418

zbMATH Keywords

unbounded domainsweighted \(L^p\) spacesgeneralized Sobolev spaces

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Asymptotic behavior of solutions to PDEs (35B40) Attractors (35B41) Second-order nonlinear hyperbolic equations (35L70) General theory of partial differential operators (47F05) A priori estimates in context of PDEs (35B45) Initial value problems for second-order hyperbolic equations (35L15) Degenerate hyperbolic equations (35L80) Strings (74K05)

Related Items (6)

Blow-up for a non-degenerate non-local quasilinear wave equation on IR^N ⋮ Attractors of the strongly damped Kirchhoff wave equation on \(\mathbb{R}^{N}\) ⋮ \( \varphi^4\) solitons in Kirchhoff wave equation ⋮ Global existence and energy decay for mildly degenerate Kirchhoff’s equations on ℝ^N ⋮ Central manifold theory for the generalized equation of Kirchhoff strings on \(\mathbb R^N\) ⋮ Existence of global solutions and stability results for a nonlinear wave problem in unbounded domains

Cites Work

• On space-time means and strong global solutions of nonlinear hyperbolic equations
• Existence of a global attractor for semilinear dissipative wave equations on \(\mathbb{R}^N\)
• Global existence, decay, and blowup of solutions for some mildly degenerate nonlinear Kirchhoff strings
• Global bifurcation results for a semilinear elliptic equation on all of \(\mathbb{R}^ N\)
• Estimates on the dimension of a global attractor for a semilinear dissipative wave equation on \(\mathbb{R}^N\)
• On Global Existence, Asymptotic Stability and Blowing Up of Solutions for Some Degenerate Non-linear Wave Equations of Kirchhoff Type with a Strong Dissipation
• Attractors for semilinear damped wave equations on 3
• Asymptotic behaviour and attractors for a semilinear damped wave equation with supercritical exponent
• Attractors of partial differential evolution equations in an unbounded domain
• Global existence and blow-up results for an equation of Kirchhoff type on \(\mathbb{R}^N\)

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