2023/11/27 by Matheus C. Bortolan, Bortolan, Matheus C., Tomás Caraballo +3
Engineering · Mathematics · Medicine · #35B41 #35L20 #37L25 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2311.15630
openalex publication_date 2023/11/27 · openalex created_date 2023/11/29 · openalex updated_date 2026/07/31
In this work we define the generalized φ-pullback attractors for evolution processes in complete metric spaces, which are compact and positively invariant families, such that they pullback attract bounded sets with a rate determined by a decreasing function φ that vanishes at infinity. We find conditions under which a given evolution process has a generalized φ-pullback attractor, both in the discrete and in the continuous cases. We present a result for the special case of generalized polynomial pullback attractors, and apply it to obtain such an object for a nonautonomous wave equation.