Vishik, M. I.; Chepyzhov, V. V. 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. Cited in 3 Documents 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 Keywords:fractal dimension; global attractors; \(\varepsilon\)-entropy; wave equations PDFBibTeX XMLCite \textit{M. I. Vishik} and \textit{V. V. Chepyzhov}, Probl. Inf. Transm. 39, No. 1, 2--20 (2003; Zbl 1072.37056); translation from Prob. Peredachi Inf. 39, No. 1, 4--23 (2003) Full Text: DOI