Averaging of equations of viscoelasticity with singularly oscillating external forces

DOI10.1016/j.matpur.2017.05.007zbMath1403.35173arXiv1607.02732OpenAlexW2963372840MaRDI QIDQ1679731

Vladimir V. Chepyzhov, Vittorino Pata, Monica Conti

Publication date: 22 November 2017

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1607.02732

zbMATH Keywords

continuous semigroupmemory kerneluniform global attractornonautonomous viscoelasticity equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Attractors (35B41) Initial-boundary value problems for second-order hyperbolic equations (35L20) Singular perturbations in context of PDEs (35B25) Nonlinear constitutive equations for materials with memory (74D10) PDEs in connection with mechanics of deformable solids (35Q74) Integro-partial differential equations (35R09) Second-order semilinear hyperbolic equations (35L71)

Related Items (6)

Non-autonomous 2D Newton-Boussinesq equation with oscillating external forces and its uniform attractor ⋮ Global attractors, exponential attractors and determining modes for the three dimensional Kelvin-Voigt fluids with ``Fading memory ⋮ Homogenization of trajectory statistical solutions for the 3D incompressible magneto-micropolar fluids ⋮ Navier-Stokes-Voigt equations with memory in 3D lacking instantaneous kinematic viscosity ⋮ Homogenisation with error estimates of attractors for damped semi-linear anisotropic wave equations ⋮ Uniform attractors of 3D Navier-Stokes-Voigt equations with memory and singularly oscillating external forces

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Attractors for infinite-dimensional non-autonomous dynamical systems
• Totally dissipative dynamical processes and their uniform global attractors
• Uniform estimates of Gronwall type
• Weakly dissipative semilinear equations of viscoelasticity
• Integral manifolds and attractors with exponential rate for nonautonomous hyperbolic equations with dissipation
• Attractors of dissipative hyperbolic equations with singularly oscillating external forces
• Averaging of nonautonomous damped wave equations with singularly oscillating external forces
• Attractors for semi-linear equations of viscoelasticity with very low dissipation
• Infinite-dimensional dynamical systems in mechanics and physics.
• Evolution equations and their trajectory attractors
• The regular attractor for the reaction-diffusion system with a nonlinearity rapidly oscillating in time and its averaging
• On non-autonomous sine-Gordon type equations with a simple global attractor and some averaging
• Attractors of the reaction-diffusion systems with rapidly oscillating coefficients and their homo\-genization.
• Attractors of non-autonomous dynamical systems and their dimension
• Traveling waves of dissipative nonautonomous hyperbolic equations in a strip
• Non-autonomous 2D Navier-Stokes system with singularly oscillating external force and its global attractor
• Asymptotic stability in viscoelasticity
• Global averaging and parametric resonances in damped semilinear wave equations
• Exponential stability in linear viscoelasticity
• Averaging of 2D Navier–Stokes equations with singularly oscillating forces
• Averaging principle for dissipative dynamical systems with rapidly oscillating right-hand sides
• Non-autonomous 2D Navier–Stokes system with a simple global attractor and some averaging problems
• Approximation of trajectories lying on a global attractor of a hyperbolic equation with exterior force rapidly oscillating in time
• Quantitative homogenization of analytic semigroups and reaction-diffusion equations with Diophantine spatial frequencies.

This page was built for publication: Averaging of equations of viscoelasticity with singularly oscillating external forces