Continuity and topological structural stability for nonautonomous random attractors

2021/11/25 by Tomás Caraballo, Caraballo, Tomás, Alexandre N. Carvalho +5 · 1 citation
Computer Science · Earth and Planetary Sciences · Engineering · #35B41 #35R60 #37B35 #37L55 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Arctic and Antarctic ice dynamics #Dynamical Systems (math.DS) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2111.13006

openalex publication_date 2021/11/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work, we study continuity and topological structural stability of attractors for nonautonomous random differential equations obtained by small bounded random perturbations of autonomous semilinear problems. First, we study existence and permanence of unstable sets of hyperbolic solutions. Then, we use this to establish lower semicontinuity of nonautonomous random attractors and to show that the gradient structure persists under nonautonomous random perturbations. Finally, we apply the abstract results in a stochastic differential equation and in a damped wave equation with a perturbation on the damping.

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