Existence of an attractor and determining modes for structurally damped nonlinear wave equations

DOI10.1016/j.physd.2017.12.001zbMath1398.35009OpenAlexW2774985432MaRDI QIDQ1990066

Varga K. Kalantarov, Bilgesu A. Bilgin

Publication date: 24 October 2018

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2017.12.001

zbMATH Keywords

global solutionglobal attractornonlinear wave equationdetermining modesstrongly damped wave equationsstructurally damped wave equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Attractors (35B41) Initial-boundary value problems for second-order hyperbolic equations (35L20) Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30)

Related Items (4)

Strong attractors for the structurally damped Kirchhoff wave models with subcritical-critical nonlinearities ⋮ Strong attractors and their stability for the structurally damped Kirchhoff wave equation with supercritical nonlinearity ⋮ Complete regularity and strong attractor for the strongly damped wave equation with critical nonlinearities on \(\mathbb{R}^3\) ⋮ Introduction to special issue: ``Nonlinear partial differential equations in mathematical fluid dynamics

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Finite-dimensional attractors for the quasi-linear strongly-damped wave equation
• Long time behavior of strongly damped nonlinear wave equations
• Infinite-dimensional dynamical systems in mechanics and physics.
• Regularity, determining modes and Galerkin methods.
• Nonlinear wave equations perturbed by viscous terms. Transl. from the Russian by M. A. Shishkova
• On the strongly damped wave equation
• Attractors for strongly damped wave equations with critical nonlinearities.
• Asymptotic regularity of solutions of singularly perturbed damped wave equations with supercritical nonlinearities
• Limiting behavior of strongly damped nonlinear wave equations
• Strichartz estimates and smooth attractors for a sub-quintic wave equation with fractional damping in bounded domains
• Sur le comportement global des solutions non-stationnaires des équations de Navier-Stokes en dimension 2
• Exponential attractor for the wave equation with structural damping and supercritical exponent
• A determining form for the two-dimensional Navier-Stokes equations: The Fourier modes case
• Existence and Asymptotic Behavior for a Strongly Damped Nonlinear Wave Equation
• Determining nodes, finite difference schemes and inertial manifolds
• Smooth attractors for strongly damped wave equations
• Longtime Behaviour of Strongly Damped Wave Equations, Global Attractors and Their Dimension
• Theory of functionals that uniquely determine the asymptotic dynamics of infinite-dimensional dissipative systems
• Estimating the number of asymptotic degrees of freedom for nonlinear dissipative systems
• On the strongly damped wave equation with constraint
• Recent progress in attractors for quintic wave equations
• Smooth attractors for the quintic wave equations with fractional damping

This page was built for publication: Existence of an attractor and determining modes for structurally damped nonlinear wave equations