The attractor of a quasilinear hyperbolic equation with dissipation in \(\mathbb{R}^n\): Dimension and \(\varepsilon\)-entropy

DOI10.1007/BF02686254zbMath0974.35016OpenAlexW2058956451MaRDI QIDQ1581446

Serguei Zelik

Publication date: 13 May 2001

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02686254

zbMATH Keywords

fractal dimensionKolmogorov \(\varepsilon\)-entropy

Mathematics Subject Classification ID

Attractors (35B41) Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30) Second-order nonlinear hyperbolic equations (35L70) Initial value problems for second-order hyperbolic equations (35L15)

Related Items (3)

Spatial and dynamical chaos generated by reaction-diffusion systems in unbounded domains ⋮ Numerical computation of \(\varepsilon\)-entropy for parabolic equations with analytic solutions ⋮ Multiparameter semigroups and attractors of reaction-diffusion equations in ${\mathbb R}^n$

Cites Work

• Attractors for damped nonlinear hyperbolic equations
• Extensive properties of the complex Ginzburg-Landau equation
• The global Cauchy problem for the critical nonlinear wave equation
• Bounded, locally compact global attractors for semilinear damped wave equations on \(\mathbb{R}^ N\)
• Kolmogorov $ \varepsilon$-entropy estimates for the uniform attractors of non-autonomous reaction-diffusion systems
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