On the public citation graph

Longtime Behaviour of Strongly Damped Wave Equations, Global Attractors and Their Dimension

https://doi.org/10.1137/0522057

0 signed · 116 inferred · view as graph

Inferred edges come from two machine sources: sweeps of open repository metadata (mostly SSRN and Zenodo), and a bulk OpenAlex citation snapshot. Every row below is labelled with the one it came from. Neither is a complete citation index — absence here is not evidence of absence.

Is this your work? Sign in with ORCID and put your name on the claims that are yours.

Claim with ORCID

Reference health. See whether every reference in this work resolves to a known work and none has been retracted — and get a dated CiteStamped badge you can embed.

See reference health

What this work says

Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1007/978-1-4684-0313-8openalex-snapshot

Infinite-Dimensional Dynamical Systems in Mechanics and Physics

inferredcites →https://doi.org/10.1016/0022-0396(83)90098-0openalex-snapshot

Limiting behavior for strongly damped nonlinear wave equations

inferredcites →https://doi.org/10.1016/0022-0396(88)90010-1openalex-snapshot

Weakly damped forced Korteweg-de Vries equations behave as a finite dimensional dynamical system in the long time

inferredcites →https://doi.org/10.1016/s0294-1449(16)30343-2openalex-snapshot

Finite dimensional behavior for weakly damped driven Schrödinger equations

inferredcites →https://doi.org/10.1080/00411458708204663openalex-snapshot

Dimension of the universal attractor describing the periodically driven Sine-Gordon equations

inferredcites →https://doi.org/10.4153/cjm-1980-049-5openalex-snapshot

Existence and Asymptotic Behavior for a Strongly Damped Nonlinear Wave Equation

What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

inferred← citeshttps://doi.org/10.2139/ssrn.4642278openalex-extracted

inferred← citeshttps://doi.org/10.1002/mma.10300openalex-snapshot

Well‐posedness for a class of wave equations with nonlocal weak damping

inferred← citeshttps://doi.org/10.1002/mma.1080openalex-snapshot

Longtime behavior for a nonlinear wave equation arising in elasto‐plastic flow

inferred← citeshttps://doi.org/10.1002/mma.4315openalex-snapshot

Attractors for the strongly damped wave equation with p‐Laplacian

inferred← citeshttps://doi.org/10.1002/mma.4504openalex-snapshot

Qualitative theory for strongly damped wave equations

inferred← citeshttps://doi.org/10.1007/bf02104572openalex-snapshot

Parabolic equations with nonlocal nonlinear source

inferred← citeshttps://doi.org/10.1007/s00028-023-00872-4openalex-snapshot

Complete regularity and strong attractor for the strongly damped wave equation with critical nonlinearities on $$\mathbb {R}^{3}$$

inferred← citeshttps://doi.org/10.1007/s000300050049openalex-snapshot

Asymptotic behavior of a semilinear problem in heat conduction with memory

inferred← citeshttps://doi.org/10.1007/s00220-004-1233-1openalex-snapshot

On the Strongly Damped Wave Equation

inferred← citeshttps://doi.org/10.1007/s00245-022-09894-9openalex-snapshot

Strong Attractors for the Structurally Damped Kirchhoff Wave Models with Subcritical-Critical Nonlinearities

inferred← citeshttps://doi.org/10.1007/s00245-023-09998-wopenalex-snapshot

Global Attractor for a Coupled Wave and Plate Equation with Nonlocal Weak Damping on Riemannian Manifolds

inferred← citeshttps://doi.org/10.1007/s00245-026-10395-2openalex-snapshot

Asymptotic Behavior of Wave Equations with Critical Nonlinearity, Nonlocal Weak Damping and Nonlinear Colored Noise

inferred← citeshttps://doi.org/10.1007/s10255-004-0192-9openalex-snapshot

The Inflated Attractors of Non–autonomous Strongly Damped Wave Equations

inferred← citeshttps://doi.org/10.1007/s10255-005-0287-yopenalex-snapshot

Global Periodic Attractor for Strongly Damped and Driven Wave Equations

inferred← citeshttps://doi.org/10.1007/s10440-008-9405-1openalex-snapshot

Estimate on the Dimension of Global Attractor for Nonlinear Dissipative Kirchhoff Equation

inferred← citeshttps://doi.org/10.1007/s10915-022-02018-zopenalex-snapshot

Exponential Integrators for Second-Order in Time Partial Differential Equations

inferred← citeshttps://doi.org/10.1007/s10915-024-02762-4openalex-snapshot

Hybridizable Discontinuous Galerkin Method for Strongly Damped Wave Problem

inferred← citeshttps://doi.org/10.1007/s10915-025-03007-8openalex-snapshot

Mixed Virtual Element Method for a Strongly Damped Wave Equation

inferred← citeshttps://doi.org/10.1007/s11587-025-00998-2openalex-snapshot

Global existence of a nonlinear coupled sine-Gordon system with Neumann boundary conditions

inferred← citeshttps://doi.org/10.1007/s11854-026-0437-0openalex-snapshot

Well-posedness, regularity and attractor for the structurally damped wave equation with supercritical nonlinearity on ℝN

inferred← citeshttps://doi.org/10.1007/s12220-024-01572-2openalex-snapshot

On Inverse Problems for a Strongly Damped Wave Equation on Compact Manifolds

inferred← citeshttps://doi.org/10.1016/j.amc.2003.08.147openalex-snapshot

Kernel sections for non-autonomous strongly damped wave equations of non-degenerate Kirchhoff-type

inferred← citeshttps://doi.org/10.1016/j.amc.2013.05.044openalex-snapshot

Exponential attractors for the strongly damped wave equation

inferred← citeshttps://doi.org/10.1016/j.aml.2024.109189openalex-snapshot

Structure preserving FEM for the perturbed wave equation of quantum mechanics

inferred← citeshttps://doi.org/10.1016/j.aml.2025.109599openalex-snapshot

Local solution becomes global solution as damping coefficient goes to infinity

inferred← citeshttps://doi.org/10.1016/j.bulsci.2026.103871openalex-snapshot

Random attractors of nonlocal weak damping wave equations driven by nonlinear colored noise

inferred← citeshttps://doi.org/10.1016/j.camwa.2018.02.002openalex-snapshot

Finite fractal dimension of random attractor for stochastic non-autonomous strongly damped wave equation

inferred← citeshttps://doi.org/10.1016/j.camwa.2025.09.002openalex-snapshot

Convergence analysis of an energy-stable linearized virtual element method for the strongly damped Klein-Gordon equation

inferred← citeshttps://doi.org/10.1016/j.cnsns.2005.06.007openalex-snapshot

One-dimensional global attractor for strongly damped wave equations

inferred← citeshttps://doi.org/10.1016/j.cnsns.2011.09.001openalex-snapshot

Random attractor of the stochastic strongly damped wave equation

inferred← citeshttps://doi.org/10.1016/j.cnsns.2012.01.025openalex-snapshot

Kolmogorov ε-entropy of attractor for a non-autonomous strongly damped wave equation

inferred← citeshttps://doi.org/10.1016/j.jde.2007.08.004openalex-snapshot

Longtime behavior of the Kirchhoff type equation with strong damping on RN

inferred← citeshttps://doi.org/10.1016/j.jde.2008.02.011openalex-snapshot

Strongly damped wave problems: Bootstrapping and regularity of solutions

inferred← citeshttps://doi.org/10.1016/j.jde.2009.04.010openalex-snapshot

Finite-dimensional attractors for the quasi-linear strongly-damped wave equation

inferred← citeshttps://doi.org/10.1016/j.jde.2010.09.024openalex-snapshot

Global attractor for the Kirchhoff type equation with a strong dissipation

inferred← citeshttps://doi.org/10.1016/j.jde.2023.04.023openalex-snapshot

Quasi-periodic traveling waves for forced Kirchhoff equations with strong damping on flat tori

inferred← citeshttps://doi.org/10.1016/j.jde.2024.01.033openalex-snapshot

Global quantitative stability of wave equations with strong and weak dampings

inferred← citeshttps://doi.org/10.1016/j.jde.2024.08.003openalex-snapshot

Inverse problems for a quasilinear strongly damped wave equation arising in nonlinear acoustics

inferred← citeshttps://doi.org/10.1016/j.jmaa.2010.09.051openalex-snapshot

Finite-dimensional attractors for the Kirchhoff equation with a strong dissipation

inferred← citeshttps://doi.org/10.1016/j.jmaa.2014.05.010openalex-snapshot

Strongly damped wave equation with exponential nonlinearities

inferred← citeshttps://doi.org/10.1016/j.jmaa.2018.09.012openalex-snapshot

Stability of attractors for the Kirchhoff wave equation with strong damping and critical nonlinearities

inferred← citeshttps://doi.org/10.1016/j.jmaa.2020.124186openalex-snapshot

Asymptotic behaviour of the wave equation with nonlocal weak damping and anti-damping

inferred← citeshttps://doi.org/10.1016/j.na.2008.02.114openalex-snapshot

Global attractor for a nonlinear wave equation arising in elastic waveguide model

inferred← citeshttps://doi.org/10.1016/j.na.2019.01.005openalex-snapshot

On wave equations of the p -Laplacian type with supercritical nonlinearities

inferred← citeshttps://doi.org/10.1016/j.nonrwa.2009.01.022openalex-snapshot

Exponential attractors for the strongly damped wave equations

inferred← citeshttps://doi.org/10.1016/j.physd.2017.12.001openalex-snapshot

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

inferred← citeshttps://doi.org/10.1016/s0022-247x(02)00006-9openalex-snapshot

Finite dimensionality and regularity of attractors for a 2-D semilinear wave equation with nonlinear dissipation

inferred← citeshttps://doi.org/10.1016/s0022-247x(02)00437-7openalex-snapshot

Kernel sections for non-autonomous strongly damped wave equations

inferred← citeshttps://doi.org/10.1016/s0096-3003(00)00080-1openalex-snapshot

The sine-Gordon equation in the finite line

inferred← citeshttps://doi.org/10.1016/s0893-9659(03)90134-0openalex-snapshot

Attractors for strongly damped wave equations with critical exponent

inferred← citeshttps://doi.org/10.1016/s0895-7177(04)90531-6openalex-snapshot

Uniform energy estimates for a semilinear evolution equation of the Mindlin-Timoshenko beam with memory

inferred← citeshttps://doi.org/10.1017/s0308210500023805openalex-snapshot

Eigenvalue problems for the wave equation with strong damping

inferred← citeshttps://doi.org/10.1051/m2an/2025042openalex-snapshot

A low-rank algorithm for strongly damped wave equations with visco-elastic damping and mass terms

inferred← citeshttps://doi.org/10.1063/1.1418719openalex-snapshot

Attractors for second-order lattice dynamical systems with damping

inferred← citeshttps://doi.org/10.1063/1.1775873openalex-snapshot

Global periodic attractor for strongly damped wave equations with time-periodic driving force

inferred← citeshttps://doi.org/10.1063/1.3085951openalex-snapshot

Global attractor for a class of Kirchhoff models

inferred← citeshttps://doi.org/10.1063/1.3303633openalex-snapshot

Global attractors and their Hausdorff dimensions for a class of Kirchhoff models

inferred← citeshttps://doi.org/10.1063/1.3477939openalex-snapshot

Finite-dimensional attractors for the Kirchhoff models

inferred← citeshttps://doi.org/10.1063/1.4905234openalex-snapshot

A note on a strongly damped wave equation with fast growing nonlinearities

inferred← citeshttps://doi.org/10.1080/00036811.2017.1413710openalex-snapshot

Robust exponential attractors for a class of non-autonomous semi-linear second-order evolution equation with memory and critical nonlinearity

inferred← citeshttps://doi.org/10.1080/00036811.2022.2091550openalex-snapshot

An inverse problem for the transmission wave equation with Kelvin–Voigt damping

inferred← citeshttps://doi.org/10.1080/00036811.2024.2426227openalex-snapshot

A Galerkin finite element method for the nonlinear strongly damped wave equation

inferred← citeshttps://doi.org/10.1080/00036819408840290openalex-snapshot

Global attractor and inertial set for the beam equation

inferred← citeshttps://doi.org/10.1080/03605302.2017.1345937openalex-snapshot

On the strongly damped wave equation with constraint

inferred← citeshttps://doi.org/10.1080/14689367.2022.2072710openalex-snapshot

Time-dependent global attractors for strongly damped wave equations with time-dependent memory kernels

inferred← citeshttps://doi.org/10.1080/17476933.2017.1419211openalex-snapshot

Determining functionals for damped nonlinear wave equations

inferred← citeshttps://doi.org/10.1088/0951-7715/19/11/008openalex-snapshot

Non-autonomous dynamics of wave equations with nonlinear damping and critical nonlinearity

inferred← citeshttps://doi.org/10.1088/0951-7715/19/7/001openalex-snapshot

Smooth attractors for strongly damped wave equations

inferred← citeshttps://doi.org/10.1088/1361-6544/aa599fopenalex-snapshot

Longtime dynamics of the quasi-linear wave equations with structural damping and supercritical nonlinearities*

inferred← citeshttps://doi.org/10.1090/s0002-9947-08-04789-2openalex-snapshot

Local well posedness, asymptotic behavior and asymptotic bootstrapping for a class of semilinear evolution equations of the second order in time

inferred← citeshttps://doi.org/10.1090/s0002-9947-2011-05373-0openalex-snapshot

Asymptotic behavior for a semilinear second order evolution equation

inferred← citeshttps://doi.org/10.1134/s1061920808030014openalex-snapshot

Robust exponential attractors for the strongly damped wave equation with memory. I

inferred← citeshttps://doi.org/10.1134/s1061920809010038openalex-snapshot

Robust exponential attractors for the strongly damped wave equation with memory. II

inferred← citeshttps://doi.org/10.1137/060663805openalex-snapshot

Uniform Attractors for Nonautonomous Wave Equations with Nonlinear Damping

inferred← citeshttps://doi.org/10.1155/2013/308616openalex-snapshot

Asymptotic Periodicity for Strongly Damped Wave Equations

inferred← citeshttps://doi.org/10.1155/2022/8264550openalex-snapshot

Pullback Attractors for a Class of Semilinear Second‐Order Nonautonomous Evolution Equations with Hereditary Characteristics

inferred← citeshttps://doi.org/10.1155/s1085337596000048openalex-snapshot

Inertial manifolds and stabilization of nonlinear beam equationswith Balakrishnan‐Taylor damping

inferred← citeshttps://doi.org/10.1186/1029-242x-2014-396openalex-snapshot

Regularity of the attractor for strongly damped wave equations with nonlinearity

inferred← citeshttps://doi.org/10.1186/1687-1847-2012-139openalex-snapshot

Existence of solutions to strongly damped quasilinear wave equations

inferred← citeshttps://doi.org/10.1186/s13661-021-01532-7openalex-snapshot

Upper semicontinuity of pullback attractors for a nonautonomous damped wave equation

inferred← citeshttps://doi.org/10.11948/2015031openalex-snapshot

RANDOM ATTRACTOR FOR NON-AUTONOMOUS STOCHASTIC STRONGLY DAMPED WAVE EQUATION ON UNBOUNDED DOMAINS

inferred← citeshttps://doi.org/10.1216/rmj-2016-46-4-1071openalex-snapshot

Asymptotic behavior of strongly damped nonlinear beam equations

inferred← citeshttps://doi.org/10.12775/tmna.2015.059openalex-snapshot

Strongly damped wave equation and its Yosida approximations

inferred← citeshttps://doi.org/10.1353/ajm.2018.0008openalex-snapshot

A model of viscoelasticity with time-dependent memory kernels

inferred← citeshttps://doi.org/10.1353/ajm.2018.0049openalex-snapshot

Viscoelasticity with time-dependent memory kernels, II: asymptotic behavior of solutions

inferred← citeshttps://doi.org/10.1512/iumj.2008.57.3266openalex-snapshot

On the strongly damped wave equation with memory

inferred← citeshttps://doi.org/10.1515/math-2025-0152openalex-snapshot

Pullback attractors for a class of second-order delay evolution equations with dispersive and dissipative terms on unbounded domain

inferred← citeshttps://doi.org/10.1515/phys-2017-0033openalex-snapshot

Conservation laws for a strongly damped wave equation

inferred← citeshttps://doi.org/10.15672/hujms.614217openalex-snapshot

Existence of random attractors for strongly damped wave equations with multiplicative noise unbounded domain

inferred← citeshttps://doi.org/10.30538/psrp-oma2019.0039openalex-snapshot

Random attractors for Stochastic strongly damped non-autonomous wave equations with memory and multiplicative noise

inferred← citeshttps://doi.org/10.3233/asy-131208openalex-snapshot

Smooth attractors for the quintic wave equations with fractional damping

inferred← citeshttps://doi.org/10.3390/fractalfract8090516openalex-snapshot

Lp(Lq)-Maximal Regularity for Damped Equations in a Cylindrical Domain

inferred← citeshttps://doi.org/10.3934/cpaa.2005.4.705openalex-snapshot

Weakly dissipative semilinear equations of viscoelasticity

inferred← citeshttps://doi.org/10.3934/dcds.2009.25.1209openalex-snapshot

On the regularity of global attractors

inferred← citeshttps://doi.org/10.3934/dcds.2024091openalex-snapshot

Finite-dimensionality of attractors for wave equations with degenerate nonlocal damping

inferred← citeshttps://doi.org/10.3934/dcds.2024119openalex-snapshot

Complete regularity and strong attractor for the structurally damped wave equation with subcritical-critical nonlinearities on $ \mathbb{R}^{N} $

inferred← citeshttps://doi.org/10.3934/dcdsb.2019027openalex-snapshot

Global existence and asymptotic behavior of global smooth solutions to the Kirchhoff equations with strong nonlinear damping

inferred← citeshttps://doi.org/10.3934/dcdsb.2021015openalex-snapshot

The global attractor for the wave equation with nonlocal strong damping

inferred← citeshttps://doi.org/10.3934/dcdss.2026202openalex-snapshot

Sine-Gordon equation with generalized positive definite memory kernels

inferred← citeshttps://doi.org/10.3934/eect.2022025openalex-snapshot

Asymptotic behavior of the wave equation with nonlocal weak damping, anti-damping and critical nonlinearity

inferred← citeshttps://doi.org/10.3934/era.2020018openalex-snapshot

Intelligent control for Euler equations based on spline method

inferred← citeshttps://doi.org/10.3934/math.2026825openalex-snapshot

Initial-boundary value problem for a nonlinear wave equation with strong damping and structural damping

inferred← citeshttps://doi.org/10.4134/jkms.2006.43.5.931openalex-snapshot

IDENTIFICATION OF CONSTANT PARAMETERS IN PERTURBED SINE-GORDON EQUATIONS

inferred← citeshttps://doi.org/10.4236/ijmnta.2015.43015openalex-snapshot

Asymptotic Behavior of Stochastic Strongly Damped Wave Equation with Multiplicative Noise

inferred← citeshttps://doi.org/10.4236/jamp.2014.28086openalex-snapshot

Uniform Exponential Attractors for Non-Autonomous Strongly Damped Wave Equations

inferred← citeshttps://doi.org/10.48550/arxiv.1306.2294openalex-snapshot

Smooth attractors for the quintic wave equations with fractional damping

inferred← citeshttps://doi.org/10.48550/arxiv.1511.02481openalex-snapshot

Upper semicontinuity of pullback attractors for damped wave equations

inferred← citeshttps://doi.org/10.48550/arxiv.1603.07536openalex-snapshot

Viscoelasticity with time-dependent memory kernels. Part II: asymptotic behavior of solutions

inferred← citeshttps://doi.org/10.48550/arxiv.1807.00650openalex-snapshot

On wave equations of the $p$-Laplacian type with supercritical nonlinearities

inferred← citeshttps://doi.org/10.48550/arxiv.2108.07395openalex-snapshot

Asymptotic behaviour of the wave equation with nonlocal weak damping, anti-damping and critical nonlinearity

Editorial review for independent work. ICSAC — the Institute for Complexity Science and Advanced Computing — runs a structured editorial panel for researchers publishing outside journals, and publishes on CiteStamp rails. Submission is free and goes through ORCID: icsacinstitute.org/submit.