Revistes Catalanes amb Accés Obert (RACO)

A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology

Jesús Ildefonso Díaz Díaz, Lourdes Tello del Castillo


We present some results on the mathematical treatment of a global two-dimensional diffusive climate model. 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. We prove the existence of bounded weak solutions via a fixed point argument. Although, the uniqueness of solutions may fail, in general, we give a uniqueness criterion in terms of the behaviour of the solution near its “ice caps”.

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