Semilinear wave equations of viscoelasticity in the minimal state framework

DOI10.3934/DCDS.2010.27.1535zbMath1198.35154OpenAlexW2015684433MaRDI QIDQ977953

Elsa M. Marchini, Vittorino Pata, Monica Conti

Publication date: 23 June 2010

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2010.27.1535

zbMATH Keywords

extended state spacehyperbolic equation with memory

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Attractors (35B41) Initial-boundary value problems for second-order hyperbolic equations (35L20) Integro-partial differential equations (45K05) One-parameter semigroups and linear evolution equations (47D06) Linear constitutive equations for materials with memory (74D05) Hyperbolicity, Lyapunov functions for infinite-dimensional dissipative dynamical systems (37L45) Integro-partial differential equations (35R09) Second-order semilinear hyperbolic equations (35L71)

Related Items (14)

Reaction-diffusion with memory in the minimal state framework ⋮ Long term dynamics of second order-in-time stochastic evolution equations with state-dependent delay ⋮ Nonclassical diffusion with memory lacking instantaneous damping ⋮ Optimal control for evolution equations with memory ⋮ Optimal control for stochastic heat equation with memory ⋮ On the stability of Timoshenko systems with Gurtin-Pipkin thermal law ⋮ Dynamics of second order in time evolution equations with state-dependent delay ⋮ Thermoelasticity of Moore–Gibson–Thompson type with history dependence in the temperature ⋮ Wave equations with memory: the minimal state approach ⋮ Existence of smooth global attractors for nonlinear viscoelastic equations with memory ⋮ Nonclassical diffusion with memory ⋮ Random attractors for damped non-autonomous wave equations with memory and white noise ⋮ A remark on nonclassical diffusion equations with memory ⋮ Exponential attractors for abstract equations with memory and applications to viscoelasticity

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