2023/03/07 by Wenjie Hu, Hu, Wenjie, Tomás Caraballo +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2303.04155
openalex publication_date 2023/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
The aim of this paper is to propose a new method to construct exponential attractors for infinite dimensional dynamical systems in Banach spaces with explicit fractal dimension. The approach is established by combing the squeezing properties and the covering of finite subspace of Banach spaces, which generalize the method established in Hilbert spaces. The constructed exponential attractors possess explicit fractal dimensions which do not depend on the entropy number but only depend on the spectrum of the linear part and Lipschitz constant of the nonlinear part. The method is especially effective for functional differential equations in Banach spaces for which sate decomposition of the linear part can be adopted to prove squeezing property. The theoretical results are applied to the retarded functional differential equation and retarded reaction-diffusion equations.