Stabilization for the vibrations modeled by the `standard linear model' of viscoelasticity

DOI10.1007/s12044-010-0038-8zbMath1202.35026OpenAlexW1979658107MaRDI QIDQ611064

Ganesh C. Gorain

Publication date: 14 December 2010

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12044-010-0038-8

zbMATH Keywords

bounded-input bounded-output stabilityuniform stabilizationexponential energy decay estimateundamped mixed boundary conditions

Mathematics Subject Classification ID

Stabilization of systems by feedback (93D15) Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Materials of strain-rate type and history type, other materials with memory (including elastic materials with viscous damping, various viscoelastic materials) (74D99)

Related Items

Asymptotic profiles and singular limits for the viscoelastic damped wave equation with memory of type I, A stability result for the vibrations given by the standard linear model with thermoelasticity of type III, Global well-posedness of the Cauchy problem for the Jordan-Moore-Gibson-Thompson equation with arbitrarily large higher-order Sobolev norms, Hölder regularity for the Moore-Gibson-Thompson equation with infinite delay, Determining kernels in linear viscoelasticity, Nonexistence of global solutions for the semilinear Moore - Gibson - Thompson equation in the conservative case, On the analyticity of the abstract MGT-Fourier system, Well-posedness and decay property for the Cauchy problem of the standard linear solid model with thermoelasticity of type III, Decay properties for the Cauchy problem of the linear JMGT-viscoelastic plate with heat conduction, On a functional equation associated with \((a, k)\)-regularized resolvent families, Mathematical analysis of memory effects and thermal relaxation in nonlinear sound waves on unbounded domains, Decay rates for the Moore-Gibson-Thompson equation with memory, WELL-POSEDNESS AND EXPONENTIAL DECAY OF THE ENERGY IN THE NONLINEAR JORDAN–MOORE–GIBSON–THOMPSON EQUATION ARISING IN HIGH INTENSITY ULTRASOUND, Regularity of solutions for a third order differential equation in Hilbert spaces, Existence of asymptotically almost periodic solutions for damped wave equations, On the Cauchy problem of the standard linear solid model with Fourier heat conduction, The Cauchy problem for the Moore-Gibson-Thompson equation in the dissipative case, A new approach to MGT-thermoviscoelasticity, A blow-up result for the semilinear Moore-Gibson-Thompson equation with nonlinearity of derivative type in the conservative case, On the analyticity of the MGT-viscoelastic plate with heat conduction, Optimal scalar products in the Moore-Gibson-Thompson equation, Well-posedness and decay property of regularity-loss type for the Cauchy problem of the standard linear solid model with Gurtin–Pipkin thermal law, Wellposedness and decay rates for the Cauchy problem of the Moore-Gibson-Thompson equation arising in high intensity ultrasound, On the Cauchy problem of the standard linear solid model with Cattaneo heat conduction

Cites Work

• Unnamed Item
• Unnamed Item
• Semigroups of linear operators and applications to partial differential equations
• A direct method for the boundary stabilization of the wave equation
• Exact controllability and boundary stabilization of torsional vibrations of an internally damped flexible space structure
• A dynamic control law for the wave equation
• Exponential energy decay estimate for the solutions of internally damped wave equation in a bounded domain
• Exact controllability and boundary stabilization of flexural vibrations of an internally damped flexible space structure.
• Boundary stabilization of nonlinear vibrations of a flexible structure in a bounded domain in \(\mathbb{R}^n\)
• The Wave Propagation Method for the Analysis of Boundary Stabilization in Vibrating Structures
• Exact Controllability, Stabilization and Perturbations for Distributed Systems
• Note on Boundary Stabilization of Wave Equations
• A Note on the Boundary Stabilization of the Wave Equation
• Rapid Boundary Stabilization of the Wave Equation
• Stabilization of Quasi-Linear Vibrations of an Inhomogeneous Beam
• Exponential energy decay estimates for the solutions of \(n\)-dimensional Kirchhoff type wave equation