A general formula for decay rates of nonlinear dissipative systems.

DOI10.1016/j.crma.2003.10.024zbMath1073.35164OpenAlexW2038580584MaRDI QIDQ1426542

Fatiha Alabau-Boussouira

Publication date: 15 March 2004

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2003.10.024

zbMATH Keywords

nonlinear feedback

Mathematics Subject Classification ID

Stabilization of systems by feedback (93D15) Initial-boundary value problems for second-order hyperbolic equations (35L20) Second-order nonlinear hyperbolic equations (35L70) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30)

Related Items (14)

A unified approach via convexity for optimal energy decay rates of finite and infinite dimensional vibrating damped systems with applications to semi-discretized vibrating damped systems ⋮ Boundary stabilisation of the wave equation in the presence of singularities ⋮ Sharp energy estimates for nonlinearly locally damped PDEs via observability for the associated undamped system ⋮ Well-posedness and stability of a hinged plate equation with a localized nonlinear structural damping ⋮ A one-step optimal energy decay formula for indirectly nonlinearly damped hyperbolic systems coupled by velocities ⋮ Strong lower energy estimates for nonlinearly damped Timoshenko beams and Petrowsky equations ⋮ Decay estimates for second order evolution equations with memory ⋮ Nonlinear stabilization of abstract systems via a linear observability inequality and application to vibrating PDE's ⋮ A general method for proving sharp energy decay rates for memory-dissipative evolution equations ⋮ New trends towards lower energy estimates and optimality for nonlinearly damped vibrating systems ⋮ A transmission problem for the Timoshenko system with one local Kelvin-Voigt damping and non-smooth coefficient at the interface ⋮ Local indirect stabilization of N-D system of two coupled wave equations under geometric conditions ⋮ Rational rates of uniform decay for strong solutions to a fluid-structure PDE system ⋮ Control and Stabilization of Degenerate Wave Equations

Cites Work

• Unnamed Item
• Unnamed Item
• Decay estimates for some semilinear damped hyperbolic problems
• Nonlinear evolution equations - global behavior of solutions
• Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping
• A new method to obtain decay rate estimates for dissipative systems with localized damping
• Decay rates for the three-dimensional linear system of thermoelasticity
• Decay of solutions of the wave equation with a local nonlinear dissipation
• Exponential Decay for The Semilinear Wave Equation with Locally Distributed Damping
• Sharp Sufficient Conditions for the Observation, Control, and Stabilization of Waves from the Boundary
• Locally Distributed Control and Damping for the Conservative Systems

This page was built for publication: A general formula for decay rates of nonlinear dissipative systems.