Publication: A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology
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1999
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Tello, L.
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Universidad de Barcelona
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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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