A necessary and sufficient condition for the existence of an exponential attractor

DOI10.2478/BF02475219zbMath1030.37053OpenAlexW2122680232MaRDI QIDQ1407205

Dalibor Pražák

Publication date: 2003

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/bf02475219

zbMATH Keywords

wave equationglobal attractorfractal dimensionnonlinear dampingexponential attractor

Mathematics Subject Classification ID

Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems (37L30) Second-order nonlinear hyperbolic equations (35L70) Inertial manifolds and other invariant attracting sets of infinite-dimensional dissipative dynamical systems (37L25)

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Cites Work

• Unnamed Item
• Global attractors for semilinear damped wave equations with supercritical exponent
• The dimension of the global attractor for dissipative reaction-diffusion systems
• Large time behavior via the method of \(\ell\)-trajectories
• On finite fractal dimension of the global attractor for the wave equation with nonlinear damping
• Exponential attractors for a nonlinear reaction-diffusion system in