Weakly coupled dynamical systems and applications

Article type: Research Article

Authors: Carrive, M. | Miranville, A. | Piétrus, A. | Rakotoson, J.M.

Affiliations: Université de Poitiers, Laboratoire d'Applications des Mathématiques, Téléport 2, Boulevard Marie et Pierre Curie, BP 30179, 86962 Chasseneuil Futuroscope cedex, France

Note: [] Corresponding author. E‐mail: miranv@wallis.univ‐poitiers.fr.

Abstract: In this article, we define a new class of dynamical systems that are not associated with semigroups and that we call weakly coupled systems (in the sense that the initial conditions for the different components of the system are not independent) and study the asymptotic behavior of such systems. In particular, we define and study the notions of global attractor, inertial manifold and exponential attractor associated with a weakly coupled system. We also consider the nonautonomous case. As an example, we study the asymptotic behavior of weakly coupled Cahn–Hilliard equations.

Keywords: weakly coupled system, global attractor, inertial manifold, exponential attractor, nonautonomous system, coupled Cahn–Hilliard equations

Journal: Asymptotic Analysis, vol. 30, no. 2, pp. 161-185, 2002