The Moore-Gibson-Thompson equation with memory in the critical case

DOI10.1016/j.jde.2016.06.025zbMath1347.35034OpenAlexW2471988666MaRDI QIDQ305431

Irena Lasiecka, Vittorino Pata, Filippo Dell'Oro

Publication date: 29 August 2016

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

Full work available at URL: https://doi.org/10.1016/j.jde.2016.06.025

zbMATH Keywords

exponential decaymemory kernelsemiuniform stability

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) One-parameter semigroups and linear evolution equations (47D06) Volterra integral equations (45D05) Linear higher-order PDEs (35G05) Abstract hyperbolic equations (35L90)

Related Items (79)

The Cauchy-Dirichlet problem for the Moore-Gibson-Thompson equation ⋮ The MGT-Fourier model in the supercritical case ⋮ Study of wave propagation in an infinite solid due to a line heat source under Moore-Gibson-Thompson thermoelasticity ⋮ Asymptotic profiles and singular limits for the viscoelastic damped wave equation with memory of type I ⋮ Global existence for the Jordan-Moore-Gibson-Thompson equation in Besov spaces ⋮ Global existence and estimates for Blackstock's model of thermoviscous flow with second sound phenomena ⋮ Optimal feedback arising in a third-order dynamics with boundary controls and infinite horizon ⋮ General decay rate for an abstract weakly dissipative Moore-Gibson-Thompson equation ⋮ Parabolic phase-lag heat conduction theories revisited ⋮ On long time behavior of Moore-Gibson-Thompson equation with molecular relaxation ⋮ Global solvability of Moore-Gibson-Thompson equation with memory arising in nonlinear acoustics ⋮ Time-fractional Moore–Gibson–Thompson equations ⋮ General decay rate for a Moore-Gibson-Thompson equation with infinite history ⋮ Asymptotic behavior of nonlinear sound waves in inviscid media with thermal and molecular relaxation ⋮ Hölder regularity for the Moore-Gibson-Thompson equation with infinite delay ⋮ On uniqueness and instability for some thermomechanical problems involving the Moore-Gibson-Thompson equation ⋮ Boundary stabilization of the linear MGT equation with partially absorbing boundary data and degenerate viscoelasticity ⋮ Fractional powers approach of operators for abstract evolution equations of third order in time ⋮ On the Moore-Gibson-Thompson equation with memory with nonconvex kernels ⋮ Moore-Gibson-Thompson thermoelasticity in the context of double porous materials ⋮ Well-posedness and general decay for Moore-Gibson-Thompson equation in viscoelasticity with delay term ⋮ A hierarchy of heat conduction laws ⋮ Analysis of a thermoelastic problem with the Moore-Gibson-Thompson microtemperatures ⋮ Mathematical modelling of laser-instigated magneto-thermo-mechanical interactions inside half-space ⋮ Nonexistence of global solutions for the semilinear Moore - Gibson - Thompson equation in the conservative case ⋮ On a fourth-order equation of Moore-Gibson-Thompson type ⋮ Continuous dependence and convergence for Moore-Gibson-Thompson heat equation ⋮ Solvability of the Moore-Gibson-Thompson equation with viscoelastic memory type II and integral condition ⋮ Well‐posedness for the fourth‐order Moore–Gibson–Thompson equation in the class of Banach‐space‐valued Hölder‐continuous functions ⋮ Well‐posedness and exponential decay for the Moore–Gibson–Thompson equation with time‐dependent memory kernel ⋮ Analysis of a Moore-Gibson-Thompson thermoelastic problem ⋮ Fractional derivative Moore‐Gibson‐Thompson heat equation without singular kernel for a thermoelastic medium with a cylindrical hole and variable properties ⋮ Global existence and general decay of Moore–Gibson–Thompson equation with not necessarily decreasing kernel ⋮ On the elimination of infinite memory effects on the stability of a nonlinear non-homogeneous rotating body-beam system ⋮ Asymptotic behaviors for the Jordan-Moore-Gibson-Thompson equation in the viscous case ⋮ Boundary controllability for the 1D Moore-Gibson-Thompson equation ⋮ Well-posedness and decay property for the Cauchy problem of the standard linear solid model with thermoelasticity of type III ⋮ A higher-order non-autonomous semilinear parabolic equation ⋮ Spectral properties of a class of operator functions with applications to the Moore-Gibson-Thompson equation with memory ⋮ Some results in Moore‐Gibson‐Thompson thermoelasticity of dipolar bodies ⋮ Nonlinear acoustic equations of fractional higher order at the singular limit ⋮ Singular Thermal Relaxation Limit for the Moore-Gibson-Thompson Equation Arising in Propagation of Acoustic Waves ⋮ New general decay result for a fourth-order Moore-Gibson-Thompson equation with memory ⋮ On the decay of MGT-viscoelastic plate with heat conduction of Cattaneo type in bounded and unbounded domains ⋮ Decay properties for the Cauchy problem of the linear JMGT-viscoelastic plate with heat conduction ⋮ New general decay results for a Moore–Gibson–Thompson equation with memory ⋮ Mathematical analysis of memory effects and thermal relaxation in nonlinear sound waves on unbounded domains ⋮ On the Jordan-Moore-Gibson-Thompson wave equation in hereditary fluids with quadratic gradient nonlinearity ⋮ Controllability results for the Moore-Gibson-Thompson equation arising in nonlinear acoustics ⋮ Unnamed Item ⋮ Decay rates for the Moore-Gibson-Thompson equation with memory ⋮ Thermoelasticity of Moore–Gibson–Thompson type with history dependence in the temperature ⋮ A general stability result for a viscoelastic Moore-Gibson-Thompson equation in the whole space ⋮ Global well-posedness of the Cauchy problem for the 3D Jordan–Moore–Gibson–Thompson equation ⋮ Spatial behaviour of solutions of the Moore-Gibson-Thompson equation ⋮ Moore-Gibson-Thompson equation with memory in a history framework: a semigroup approach ⋮ Unnamed Item ⋮ A note on the Moore-Gibson-Thompson equation with memory of type II ⋮ Reconstructing the Moore-Gibson-Thompson equation ⋮ On long-time behavior of Moore-Gibson-Thompson equation with localized and degenerate memory effect ⋮ On the Cauchy problem of the standard linear solid model with Fourier heat conduction ⋮ Feedback control of the acoustic pressure in ultrasonic wave propagation ⋮ The Cauchy problem for the Moore-Gibson-Thompson equation in the dissipative case ⋮ A new approach to MGT-thermoviscoelasticity ⋮ General decay of the Cauchy problem for a Moore-Gibson-Thompson equation with memory ⋮ Vanishing relaxation time dynamics of the Jordan Moore-Gibson-Thompson equation arising in nonlinear acoustics ⋮ A blow-up result for the semilinear Moore-Gibson-Thompson equation with nonlinearity of derivative type in the conservative case ⋮ Optimal decay rate for the Cauchy problem of the standard linear solid model with Gurtin-Pipkin thermal law ⋮ Well-posedness and long time behavior for a general class of Moore-Gibson-Thompson equations with a memory ⋮ On the analyticity of the MGT-viscoelastic plate with heat conduction ⋮ Well-posedness and decay property of regularity-loss type for the Cauchy problem of the standard linear solid model with Gurtin–Pipkin thermal law ⋮ The Inviscid Limit of Third-Order Linear and Nonlinear Acoustic Equations ⋮ On the time decay for the MGT-type porosity problems ⋮ Boundary feedback stabilization of a critical nonlinear JMGT equation with Neumann-undissipated part of the boundary ⋮ On the well-posedness and general decay results of Moore-Gibson-Thompson equation with memory ⋮ Well-posedness and stability for a Moore-Gibson-Thompson equation with internal distributed delay ⋮ On the decay of the energy for radial solutions in Moore–Gibson–Thompson thermoelasticity ⋮ Exterior controllability properties for a fractional Moore-Gibson-Thompson equation ⋮ On the Cauchy problem of the standard linear solid model with Cattaneo heat conduction

Cites Work

• Moore-Gibson-Thompson equation with memory. I: Exponential decay of energy
• Second-sound phenomena in inviscid, thermally relaxing gases
• Moore-Gibson-Thompson equation with memory. II: General decay of energy.
• Stability and exponential stability in linear viscoelasticity
• Optimal regularity and long-time behavior of solutions for the Westervelt equation
• Non-uniform stability for bounded semi-groups on Banach spaces
• Semigroups of linear operators and applications to partial differential equations
• Propagation of ultrasonic sound waves in dissipative dilute gases and extended irreversible thermodynamics
• Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping
• Global solvability of Moore-Gibson-Thompson equation with memory arising in nonlinear acoustics
• Energy decay rates for the semilinear wave equation with nonlinear localized damping and source terms
• Asymptotic stability in viscoelasticity
• Mathematical Control Theory of Coupled PDEs
• An analysis of nonhomogeneous Kuznetsov's equation: Local and global well-posedness; exponential decay
• On the Spectrum of C 0 -Semigroups
• Tauberian Theorems and Stability of One-Parameter Semigroups
• A Note on Weak Stabilizability of Contraction Semigroups
• An abstract semigroup approach to the third‐order Moore–Gibson–Thompson partial differential equation arising in high‐intensity ultrasound: structural decomposition, spectral analysis, exponential stability
• WELL-POSEDNESS AND EXPONENTIAL DECAY OF THE ENERGY IN THE NONLINEAR JORDAN–MOORE–GIBSON–THOMPSON EQUATION ARISING IN HIGH INTENSITY ULTRASOUND
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The Moore-Gibson-Thompson equation with memory in the critical case