Asymptotic stability for nonlinear damped Kirchhoff systems involving the fractional \(p\)-Laplacian operator

DOI10.1016/j.jde.2017.02.039zbMath1368.35034OpenAlexW2612897475MaRDI QIDQ2358704

Sara Saldi, Patrizia Pucci

Publication date: 15 June 2017

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2017.02.039

zbMATH Keywords

homogeneous Dirichlet boundary conditionslocal and global asymptotic stabilitytime-dependent nonlinear damping forcesdissipative Kirchhoff systems

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order hyperbolic equations (35L20) Stability in context of PDEs (35B35) Second-order nonlinear hyperbolic equations (35L70) Degenerate hyperbolic equations (35L80) PDEs in connection with mechanics of deformable solids (35Q74) Fractional partial differential equations (35R11)

Related Items (23)

Multiplicity and asymptotic behavior of solutions to a class of Kirchhoff-type equations involving the fractional \(p\)-Laplacian ⋮ Dynamics of nonlinear hyperbolic equations of Kirchhoff type ⋮ Sign-changing solutions of fractional $p$-Laplacian problems ⋮ Stability for the wave equation in an unbounded domain with finite measure and with nonlinearities of arbitrary growth ⋮ Global existence and energy decay for a coupled system of Kirchhoff beam equations with weakly damping and logarithmic source ⋮ Energy-based localization of positive solutions for stationary Kirchhoff-type equations and systems ⋮ Maximum principles and qualitative properties of solutions for nonlocal double phase operator ⋮ Long-time dynamics of Kirchhoff equations with exponential nonlinearities ⋮ On a class of fractional p (⋅,⋅)−Laplacian problems with sub-supercritical nonlinearities ⋮ On nonlinear Schrödinger equations on the hyperbolic space ⋮ Fractional double-phase patterns: concentration and multiplicity of solutions ⋮ On the nonlinear Schrödinger equation on the Poincaré ball model ⋮ A problem involving a nonlocal operator ⋮ Qualitative analysis for a degenerate Kirchhoff-type diffusion equation involving the fractional \(p\)-Laplacian ⋮ Solutions for a Kirchhoff equation with critical Caffarelli-Kohn-Nirenberg growth and discontinuous nonlinearity ⋮ Multiplicity of solutions for variable-order fractional Kirchhoff equations with nonstandard growth ⋮ Stability for extensible beams with a single degenerate nonlocal damping of Balakrishnan-Taylor type ⋮ Attractors for the degenerate Kirchhoff wave model with strong damping: existence and the fractal dimension ⋮ Editorial. Progress in nonlinear Kirchhoff problems ⋮ Kirchhoff-type problems on a geodesic ball of the hyperbolic space ⋮ Lifespan of solutions to a hyperbolic type Kirchhoff equation with arbitrarily high initial energy ⋮ On the bounds of the sum of eigenvalues for a Dirichlet problem involving mixed fractional Laplacians ⋮ Blow-up of solutions to a viscoelastic wave equation with nonlocal damping

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