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

Abstract

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 equation was initially suggested by North and Cahalan (following a previous deterministic model 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 ).