On the nonlinear boundary stabilization of Kirchhoff plates

DOI10.1007/BF01194984zbMath0818.35126MaRDI QIDQ1346270

Vilmos Komornik

Publication date: 20 August 1995

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

zbMATH Keywords

integral inequalityenergy decay ratefeedback function

Mathematics Subject Classification ID

Related Items (25)

The existence and the asymptotic behavior of a plate equation with frictional damping and a logarithmic source term ⋮ Existence and a general decay results for a viscoelastic plate equation with a logarithmic nonlinearity ⋮ General decay for weak viscoelastic Kirchhoff plate equations with delay boundary conditions ⋮ Stabilization of a suspension bridge with locally distributed damping ⋮ Existence and general decay estimate for a nonlinear plate problem ⋮ General decay for Kirchhoff plates with a boundary condition of memory type ⋮ Energy decay of dissipative plate equations with memory-type boundary conditions ⋮ Global existence and asymptotic behaviour for a viscoelastic plate equation with nonlinear damping and logarithmic nonlinearity ⋮ Blow-up phenomena for a damped plate equation with logarithmic nonlinearity ⋮ Stability properties of dissipative evolution equations with nonautonomous and nonlinear damping ⋮ A boundary condition with memory for Kirchhoff plate equations. ⋮ Kirchhoff plates with viscous boundary dissipation ⋮ Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term ⋮ Existence, nonexistence, and stability of solutions for a delayed plate equation with the logarithmic source ⋮ On the asymptotic stability for Kirchhoff plates with viscoelastic dissipation ⋮ Viscoelastic plate equation with boundary feedback ⋮ Stability for the Kirchhoff plates equations with viscoelastic boundary conditions in noncylindrical domains ⋮ Plate equations with viscoelastic boundary damping ⋮ Decay rate of a weakly dissipative viscoelastic plate equation with infinite memory ⋮ Well-posedness and asymptotic stability results for a viscoelastic plate equation with a logarithmic nonlinearity ⋮ New general decay results for a von Karman plate equation with memory-type boundary conditions ⋮ Uniform decay rates for a suspension bridge with locally distributed nonlinear damping ⋮ General decay rate of a weakly dissipative viscoelastic equation with a general damping ⋮ Optimal decay result for Kirchhoff plate equations with nonlinear damping and very general type of relaxation functions ⋮ Plate equations with frictional and viscoelastic dampings

Cites Work

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• Stabilization of wave and plate-like equations with nonlinear dissipation on the boundary
• A direct method for the boundary stabilization of the wave equation
• Exponential decay rates for the solutions of Euler-Bernoulli equations with boundary dissipation occuring in the moments only
• On the nonlinear boundary stabilization of the wave equation
• Stabilization of Kirchhoff plate equation in star-shaped domain by nonlinear boundary feedback

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