### Impacto

Díaz Díaz, Jesús Ildefonso and Bermejo, R. and Carpio, Jaime and Tello, J. Ignacio
(2009)
*Mathematical and numerical analysis of a nonlinear diffusive climate energy balance model.*
Mathematical and Computer Modelling, 49
(5-6).
pp. 1180-1210.
ISSN 0895-7177

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Official URL: http://www.sciencedirect.com/science/article/pii/S0895717708001386

## Abstract

The purpose of this paper is to carry out the mathematical and numerical analysis of a two-dimensional nonlinear parabolic problem on a compact Riemannian manifold without boundary, which arises in the energy balance for the averaged surface temperature. We use a possibly quasi-linear diffusion operator suggested by P. H. Stone in 1972. The modelling of the Budyko discontinuous coalbedo is formulated in terms of a bounded maximal monotone graph of R(2). The existence of global solutions is proved by applying a fixed point argument. Since the uniqueness of solutions may fail for the case of discontinuous coalbedo, we introduce the notion of non-degenerate solutions and show that the problem has at most one solution in this class of functions. The numerical analysis is carried out for the special case of a spherical Earth and uses quasi-uniform spherical triangles as finite elements. We study the existence, uniqueness and stability of the approximate solutions. We also show results of some long-term numerical experiments.

Item Type: | Article |
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Uncontrolled Keywords: | parabolic p-laplacian; approximation; equations; climate; nonlinear diffusive energy balance model; non-degenerate solution; finite elements; 2-sphere |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 15131 |

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Deposited On: | 08 May 2012 08:53 |

Last Modified: | 06 Feb 2014 10:17 |

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