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.
@article{urn:eudml:doc:42590,
title = {A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology.},
journal = {Collectanea Mathematica},
volume = {50},
year = {1999},
pages = {19-51},
zbl = {0936.35095},
mrnumber = {MR1701215},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:42590}
}
Díaz, J. I.; Tello, L. A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology.. Collectanea Mathematica, Tome 50 (1999) pp. 19-51. http://gdmltest.u-ga.fr/item/urn:eudml:doc:42590/