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

Díaz, J. I., and Tello, L.. "A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology.." Collectanea Mathematica 50.1 (1999): 19-51. <http://eudml.org/doc/42590>.

@article{Díaz1999,
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.},
author = {Díaz, J. I., Tello, L.},
journal = {Collectanea Mathematica},
keywords = {Variedad riemanniana; Ecuaciones parabólicas; Dominios no acotados; Difusión no lineal; Climatología; Problemas bidimensionales; long time averaged energy balance; existence of bounded weak solutions; fixed point argument; uniqueness criterion},
language = {eng},
number = {1},
pages = {19-51},
title = {A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology.},
url = {http://eudml.org/doc/42590},
volume = {50},
year = {1999},
}

TY - JOUR
AU - Díaz, J. I.
AU - Tello, L.
TI - A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology.
JO - Collectanea Mathematica
PY - 1999
VL - 50
IS - 1
SP - 19
EP - 51
AB - 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.
LA - eng
KW - Variedad riemanniana; Ecuaciones parabólicas; Dominios no acotados; Difusión no lineal; Climatología; Problemas bidimensionales; long time averaged energy balance; existence of bounded weak solutions; fixed point argument; uniqueness criterion
UR - http://eudml.org/doc/42590
ER -