Kolmogorov $\varepsilon$-entropy of the uniform attractor for a wave equation

TL;DR

This paper establishes an upper bound for the -entropy of the uniform attractor of a non-autonomous semilinear wave equation in three dimensions, even when external forces lack translation-compactness, advancing understanding of attractor complexity.

Contribution

It introduces a novel approach using weak topology entropy to estimate the -entropy of the uniform attractor under non-translation-compact external forces.

Findings

Derived an upper bound for the -entropy of the attractor.

Extended entropy estimates to non-translation-compact external forces.

Provided new insights into the complexity of wave equation attractors.

Abstract

This paper is concerned with a non-autonomous sup-cubic semilinear wave equation in a smooth bounded domain of $\mathbb R^{3}$, using the introduced weak topology entropy, we obtain an upper bound for the $\varepsilon$-entropy of the uniform attractor for the case where the external forces are not translation-compact.