Differential and Integral Equations

Infinite-dimensional attractors for evolution equations with $p$-Laplacian and their Kolmogorov entropy

Messoud A. Efendiev and Mitsuharu Ôtani

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In this paper we give a detailed study on the attractors for the parabolic equations in bounded domains involving $p$-Laplacian as the principal term. Not only the existence of attractors but also their new properties are presented, which cannot be observed for the non-degenerate parabolic equations. In particular, we construct infinite-dimensional attractors whose $\varepsilon$-Kolmogorov entropy behave as the polynomial of $1/\varepsilon$ as $\varepsilon$ tends to zero.

Article information

Differential Integral Equations, Volume 20, Number 11 (2007), 1201-1209.

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 37L30: Attractors and their dimensions, Lyapunov exponents
Secondary: 35B41: Attractors 35K55: Nonlinear parabolic equations 35K65: Degenerate parabolic equations


Efendiev, Messoud A.; Ôtani, Mitsuharu. Infinite-dimensional attractors for evolution equations with $p$-Laplacian and their Kolmogorov entropy. Differential Integral Equations 20 (2007), no. 11, 1201--1209. https://projecteuclid.org/euclid.die/1356039284

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