Dimension of the global attractor for strongly damped nonlinear wave equation

DOI10.1006/jmaa.1999.6269zbMath0928.35105OpenAlexW2085217144MaRDI QIDQ1289038

Shengfan Zhou

Publication date: 12 January 2000

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1999.6269

zbMATH Keywords

Hausdorff dimension

Mathematics Subject Classification ID

Semigroups of nonlinear operators (47H20) Initial-boundary value problems for second-order hyperbolic equations (35L20) Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Second-order nonlinear hyperbolic equations (35L70)

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Exponential attractors for the strongly damped wave equations with critical exponent ⋮ Attractors for second-order lattice dynamical systems with damping ⋮ Long time behavior for the visco-elastic damped wave equation in \(\mathbb{R}^n_+\) and the boundary effect ⋮ Invariant set and attractor of nonautonomous functional differential systems. ⋮ Random attractor of the stochastic strongly damped wave equation ⋮ RANDOM ATTRACTOR FOR NON-AUTONOMOUS STOCHASTIC STRONGLY DAMPED WAVE EQUATION ON UNBOUNDED DOMAINS ⋮ Kolmogorov \(\varepsilon \)-entropy of attractor for a non-autonomous strongly damped wave equation ⋮ Random attractor for a stochastic damped wave equation with multiplicative noise on unbounded domains ⋮ Finite fractal dimension of random attractor for stochastic non-autonomous strongly damped wave equation ⋮ Asymptotic behavior of solutions for initial-boundary value problems for strongly damped nonlinear wave equations ⋮ Global attractor for a strongly damped wave equation with fully supercritical nonlinearities ⋮ Random attractors for stochastic retarded strongly damped wave equations with additive noise on bounded domains ⋮ Pointwise long time behavior for the mixed damped nonlinear wave equation in \(\mathbb{R}^n_+\) ⋮ Kernel sections for non-autonomous strongly damped wave equations.

Cites Work

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• Semigroups of linear operators and applications to partial differential equations
• Infinite-dimensional dynamical systems in mechanics and physics
• Limiting behavior of strongly damped nonlinear wave equations
• Existence and Asymptotic Behavior for a Strongly Damped Nonlinear Wave Equation
• Dimension of the global attractor for the damped and driven sine-Gordon equation
• On the dimension of the global attractor for the damped Sine–Gordon equation

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