Decay of solutions of the wave equation with arbitrary localized nonlinear damping

DOI10.1016/j.jde.2004.12.010zbMath1073.35166OpenAlexW2001013647MaRDI QIDQ1775526

Mourad Bellassoued

Publication date: 4 May 2005

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

Full work available at URL: https://doi.org/10.1016/j.jde.2004.12.010

zbMATH Keywords

wave equationinitial-boundary value problemDirichlet conditionsdecay rateFBI transformlogarithmic decaylocalized nonlinear dampingsmooth Riemannian compact manifold

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Initial-boundary value problems for second-order hyperbolic equations (35L20) Second-order nonlinear hyperbolic equations (35L70) Hyperbolic equations on manifolds (58J45)

Related Items (13)

Asymptotic stability for nonlinear damped Kirchhoff systems involving the fractional \(p\)-Laplacian operator ⋮ Stabilization of the nonlinear damped wave equation via linear weak observability ⋮ Exponential decay for semilinear wave equation with localized damping in the hyperbolic space ⋮ A one-step optimal energy decay formula for indirectly nonlinearly damped hyperbolic systems coupled by velocities ⋮ Boundary stabilization of a semilinear wave equation with variable coefficients under the time-varying and nonlinear feedback ⋮ Energy decay for the elastic wave equation with a local time-dependent nonlinear damping ⋮ Energy decay rates for solutions of the wave equations with nonlinear damping in exterior domain ⋮ Uniform attractor for non-autonomous plate equation with a localized damping and a critical nonlinearity ⋮ Unified approach to stabilization of waves on compact surfaces by simultaneous interior and boundary feedbacks of unrestricted growth ⋮ Energy decay rates for the semilinear wave equation with nonlinear localized damping and source terms ⋮ Rate of decay of solutions of the wave equation with arbitrary localized nonlinear damping ⋮ Simultaneous and indirect control of waves: Some recent developments and open problems ⋮ Stabilization of the wave equation with a localized nonlinear strong damping

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