Asymptotic behaviour of quasi-autonomous dissipative systems in Hilbert spaces

Abstract

By suitably modifying the methods used by B. Djafari Rouhani (“Ergodic Theorems for Non-expansive Sequences in Hilbert Spaces and Related Problems,” Part I, pp. 1–76, Thesis, Yale University, and “A New Proof of the weak Convergence Theorems for Non-expansive Sequences and Curves in Hilbert Spaces,” preprint, 1984) and by B. Djafari Rouhani and S. Kakutani (“Ergodic Theorems for Non-expansive Non-linear operators in a Hilbert Space,” preprint, 1984) we study the asymptotic behaviour of the quasi-autonomous dissipative system du dt + Au ∋ ƒ , where A is a monotone operator in a Hilbert space H and ƒ ϵ L 1((0, +∞); H) .