Optimal decay result for Kirchhoff plate equations with nonlinear damping and very general type of relaxation functions

DOI10.1186/s13661-019-1196-yOpenAlexW2947517298WikidataQ127962435 ScholiaQ127962435MaRDI QIDQ2108294

Adel M. Al-Mahdi

Publication date: 19 December 2022

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13661-019-1196-y

zbMATH Keywords

convexityplate equationsviscoelasticoptimal decay

Mathematics Subject Classification ID

Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) (74Dxx) Hyperbolic equations and hyperbolic systems (35Lxx) Qualitative properties of solutions to partial differential equations (35Bxx)

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Cites Work

• Unnamed Item
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• Energy decay for a viscoelastic Kirchhoff plate equation with a delay term
• General decay for a wave equation of Kirchhoff type with a boundary control of memory type
• General decay for Kirchhoff plates with a boundary condition of memory type
• Well posedness and asymptotic behavior of a coupled system of nonlinear viscoelastic equations
• Existence and sharp decay rate estimates for a von Karman system with long memory
• On the control of the wave equation by memory-type boundary condition
• General and optimal decay for a quasilinear viscoelastic equation
• Asymptotic stability of abstract dissipative systems with infinite memory
• General decay of the solution energy in a viscoelastic equation with a nonlinear source
• On the control of solutions of viscoelastic equations with boundary feedback
• Exponential decay rates for the solutions of Euler-Bernoulli equations with boundary dissipation occuring in the moments only
• Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping
• On the nonlinear boundary stabilization of Kirchhoff plates
• Decay rates for viscoelastic plates with memory
• A boundary condition with memory for Kirchhoff plate equations.
• Existence, uniqueness and stabilization for a nonlinear plate system with nonlinear damping
• Fractional Schrödinger-Poisson-Kirchhoff type systems involving critical nonlinearities
• Existence and a general decay result for a plate equation with nonlinear damping and a logarithmic source term
• Decay of solutions of the wave equation with a local nonlinear dissipation
• Coupled second order semilinear evolution equations indirectly damped via memory effects
• Plate equations with viscoelastic boundary damping
• General decay for weak viscoelastic Kirchhoff plate equations with delay boundary conditions
• Asymptotic stability for the second order evolution equation with memory
• Decay estimates for second order evolution equations with memory
• General decay of solutions of a viscoelastic equation
• Energy decay estimates for the damped plate equation with a local degenerated dissipation
• Stabilization of Bernoulli--Euler Beams by Means of a Pointwise Feedback Force
• Energy decay of dissipative plate equations with memory-type boundary conditions
• General decay for quasilinear viscoelastic equations with nonlinear weak damping
• Optimal decay rates for the viscoelastic wave equation
• Exponential Decay for The Semilinear Wave Equation with Locally Distributed Damping
• General decay rate estimate for a viscoelastic equation with weakly nonlinear time-dependent dissipation and source terms
• Intrinsic Decay Rate Estimates for Semilinear Abstract Second Order Equations with Memory
• GLOBAL EXISTENCE AND ASYMPTOTIC STABILITY FOR THE NONLINEAR AND GENERALIZED DAMPED EXTENSIBLE PLATE EQUATION
• Note on intrinsic decay rates for abstract wave equations with memory
• A boundary condition with memory for the Kirchhoff plate equations with non‐linear dissipation
• General decay of energy for a viscoelastic equation with nonlinear damping
• Uniform decay rates for viscoelastic dissipative systems

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