Moore-Gibson-Thompson equation with memory in a history framework: a semigroup approach

DOI10.1007/s00033-018-0999-5zbMath1402.35082OpenAlexW2884241314WikidataQ129465170 ScholiaQ129465170MaRDI QIDQ1990743

M. O. Alves, Arthur Henrique Caixeta, José H. Rodrigues, Marcio Antonio Jorge da Silva

Publication date: 25 October 2018

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00033-018-0999-5

zbMATH Keywords

stabilityexponential decaymemoryMoore-Gibson-Thompson equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) One-parameter semigroups and linear evolution equations (47D06) Initial value problems for linear higher-order PDEs (35G10) Higher-order hyperbolic equations (35L25) Integro-partial differential equations (35R09)

Related Items (22)

The Cauchy-Dirichlet problem for the Moore-Gibson-Thompson equation ⋮ Asymptotic profiles and singular limits for the viscoelastic damped wave equation with memory of type I ⋮ 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 ⋮ On the Moore-Gibson-Thompson equation with memory with nonconvex kernels ⋮ Nonexistence of global solutions for the semilinear Moore - Gibson - Thompson equation in the conservative case ⋮ Well‐posedness and exponential decay for the Moore–Gibson–Thompson equation with time‐dependent memory kernel ⋮ Well-posedness and decay property for the Cauchy problem of the standard linear solid model with thermoelasticity of type III ⋮ 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 ⋮ Decay properties for the Cauchy problem of the linear JMGT-viscoelastic plate with heat conduction ⋮ Unnamed Item ⋮ Decay rates for the Moore-Gibson-Thompson equation with memory ⋮ A note on the Moore-Gibson-Thompson equation with memory of type II ⋮ The Cauchy problem for the Moore-Gibson-Thompson equation in the dissipative case ⋮ General decay of the Cauchy problem for a Moore-Gibson-Thompson equation with memory ⋮ 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 ⋮ The Inviscid Limit of Third-Order Linear and Nonlinear Acoustic Equations ⋮ On the well-posedness and general decay results of Moore-Gibson-Thompson equation with memory

Cites Work

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• Global solvability of Moore-Gibson-Thompson equation with memory arising in nonlinear acoustics
• Timoshenko systems with fading memory
• Asymptotic stability in viscoelasticity
• Wave propagation in rods of Voigt material and visco-elastic materials with three-parameter models
• On the Spectrum of C 0 -Semigroups
• Spectral Theory for Contraction Semigroups on Hilbert Space

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