On the asymptotic behaviour of solutions of a stochastic energy balance climate model (Q2389367)

The existence of a random global attractor for the multi-valued random dynamical system associated to a non-linear multi-valued parabolic equation with a stochastic term of amplitude of the order of \(\varepsilon \) is investigated. The underlying equation was initially suggested by North and Cahalan (following a 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. Moreover, convergence of the global attractors when \(\varepsilon \rightarrow 0\) is verified.