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

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Díaz Díaz, Jesús Ildefonso and Tello, L. (1999) A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology. Collectanea Mathematica, 50 (1). pp. 19-51. ISSN 0010-0757

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Official URL: http://collectanea.ub.edu/index.php/Collectanea/article/view/3958/4807


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Abstract

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”.


Item Type:Article
Subjects:Sciences > Mathematics > Differential equations
ID Code:33160
Deposited On:24 Sep 2015 06:44
Last Modified:12 Dec 2018 15:07

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