
Resumo: The main objective of this talk is to present a model for hyperbolic evolution equations that pertain to extensible beams with a nonlocal, potentially degenerate damping coefficient of the Balakrishnan-Taylor type. The peculiar damping structure prevents any form of exponential behavior within the weak phase space over time, while allowing for an inherent polynomial range of stability as proved for the corresponding Lyapunov functional. Consequently, we give a preliminary examination of the long-term behavior of the associated dynamical system by analyzing the Kolmogorov ε-entropy of the family of compact attractors.
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