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On a stochastic parabolic PDE arising in climatology. (English) Zbl 1011.60044

The energy balance models considered in the paper under review describe the meridional change of temperature together with a south-north heat flux by the balance of absorbed and emitted radiative energy of the earth, in the form of set-valued stochastic PDE. As opposed to previous papers of the first author on the same subject, the system is forced by a space-time white noise. In contrast to a former paper by North and Calahan the absorbed energy functional contains a greyness factor which is supposed to be set-valued. Questions of existence and uniqueness of solutions in this framework are discussed. The stochastic perturbation acts in a stabilizing way: deterministic non-uniqueness phenomena are seen to vanish as the noise is turned on.

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R60 PDEs with randomness, stochastic partial differential equations
86A99 Geophysics
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