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On a climatological energy balance model with continents distribution

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  • We present some results on the mathematical treatment of a global two-dimensional diffusive climate model with land - sea distribution. The model is based on a long time averaged energy balance and leads to a nonlinear parabolic equation for the averaged surface temperature. The spatial domain is a compact two-dimensional Riemannian manifold without boundary simulating the Earth surface with land - sea configuration. In the oceanic areas the model is coupled with a deep ocean model. The coupling is given by a dynamic and diffusive boundary condition. We study the existence of a bounded weak solution and its numerical approximation.
    Mathematics Subject Classification: Primary: 35K55, 65M08; Secondary: 35R01, 35K92, 35R70.


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