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

Collectanea Mathematica (1999)

- Volume: 50, Issue: 1, page 19-51
- ISSN: 0010-0757

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topDíaz, 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 -

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