%0 Journal Article
%A Díaz Díaz, Jesús Ildefonso
%A Tello, L.
%T A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology
%D 1999
%@ 0010-0757
%U https://hdl.handle.net/20.500.14352/59742
%X We present some results on the mathematical treatment of a global twodimensional 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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