On the asymptotic behaviour of solutions of a stochastic energy balance climate model

We prove the existence of a random global attractor for the multivalued random dynamical system associated to a nonlinear multivalued parabolic equation with a stochastic term of amplitude of the order of ε. The equationwas initially suggested by North and Cahalan (following a previous deterministicmodel proposed by M.I. Budyko), for the modeling of some non-deterministic variability (as, for instance, the cyclones which can be treated as a fast varying component and are represented as a white-noise process) in the context of energy balance climate models. We also prove the convergence (in some sense) of the global attractors, when ε→ 0, i.e., the convergence to the global attractor for the associated deterministic case (ε = 0). © 2009 Elsevier B.V. All rights reserved.