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

  1. Tello del Castillo, Lourdes
  2. Díaz Díaz, Jesús Ildefonso
Revista:
Collectanea mathematica

ISSN: 0010-0757

Any de publicació: 1999

Volum: 50

Fascicle: 1

Pàgines: 19-52

Tipus: Article

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Altres publicacions en: Collectanea mathematica

Resum

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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