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Kolmogorov \(\varepsilon\)-entropy in the problems on global attractors for evolution equations of mathematical physics. (English. Russian original) Zbl 1072.37056

Probl. Inf. Transm. 39, No. 1, 2-20 (2003); translation from Prob. Peredachi Inf. 39, No. 1, 4-23 (2003).
Summary: We study the Kolmogorov \(\varepsilon\)-entropy and the fractal dimension of global attractors for autonomous and nonautonomous equations of mathematical physics. We prove upper estimates on the \(\varepsilon\)-entropy and fractal dimension of the global attractors of nonlinear dissipative wave equations.

MSC:

37L30 Attractors and their dimensions, Lyapunov exponents for infinite-dimensional dissipative dynamical systems
35B41 Attractors
35L70 Second-order nonlinear hyperbolic equations
35Q53 KdV equations (Korteweg-de Vries equations)
37C45 Dimension theory of smooth dynamical systems
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