On a fourth-order equation of Moore-Gibson-Thompson type

DOI10.1007/s00032-017-0270-0zbMath1383.35054OpenAlexW2759349916MaRDI QIDQ1691716

Filippo Dell'Oro, Vittorino Pata

Publication date: 25 January 2018

Published in: Milan Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00032-017-0270-0

zbMATH Keywords

exponential stabilitysolution semigrouphomogeneous Dirichlet boundary conditiongrowth boundequation with memory

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) One-parameter semigroups and linear evolution equations (47D06) Linear constitutive equations for materials with memory (74D05) Initial-boundary value problems for linear higher-order PDEs (35G16)

Related Items (27)

Asymptotic profiles and singular limits for the viscoelastic damped wave equation with memory of type I ⋮ General decay rate for a Moore-Gibson-Thompson equation with infinite history ⋮ 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 ⋮ A note on the spectral analysis of some fourth-order differential equations with a semigroup approach ⋮ A hierarchy of heat conduction laws ⋮ 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 ⋮ Analysis of a Moore-Gibson-Thompson thermoelastic problem ⋮ Spectral analysis and stability of the Moore-Gibson-Thompson-Fourier model ⋮ Solution blow-up for a fractional fourth-order equation of Moore-Gibson-Thompson type with nonlinearity nonlocal in time ⋮ 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 ⋮ New general decay results for a Moore–Gibson–Thompson equation with memory ⋮ Controllability results for the Moore-Gibson-Thompson equation arising in nonlinear acoustics ⋮ Unnamed Item ⋮ 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 ⋮ Spatial behaviour of solutions of the Moore-Gibson-Thompson equation ⋮ A note on the Moore-Gibson-Thompson equation with memory of type II ⋮ A new approach to MGT-thermoviscoelasticity ⋮ On the analyticity of the MGT-viscoelastic plate with heat conduction ⋮ 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 ⋮ 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

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Moore-Gibson-Thompson equation with memory. I: Exponential decay of energy
• The Moore-Gibson-Thompson equation with memory in the critical case
• Second-sound phenomena in inviscid, thermally relaxing gases
• Moore-Gibson-Thompson equation with memory. II: General decay of energy.
• On the Moore-Gibson-Thompson equation and its relation to linear viscoelasticity
• Semigroups of linear operators and applications to partial differential equations
• Asymptotic stability in viscoelasticity
• UNIFORM DECAY PROPERTIES OF LINEAR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS
• 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

This page was built for publication: On a fourth-order equation of Moore-Gibson-Thompson type