A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology
- Tello del Castillo, Lourdes
- Díaz Díaz, Jesús Ildefonso
ISSN: 0010-0757
Year of publication: 1999
Volume: 50
Fascicle: 1
Pages: 19-52
Type: Article
More publications in: Collectanea mathematica
Abstract
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”.