Abstract
In this paper we extend the theory of exponential attractors from the Hilbert space setting in [4] to the Banach space setting. No squeezing conditions are needed; the only requirements are for the semiflow to be C 1 in some absorbing ball, and for the linearized semiflow at every point inside the absorbing ball to split into the sum of a compact operator plus a contraction.
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Dung, L., Nicolaenko, B. Exponential Attractors in Banach Spaces. Journal of Dynamics and Differential Equations 13, 791–806 (2001). https://doi.org/10.1023/A:1016676027666
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DOI: https://doi.org/10.1023/A:1016676027666