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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.

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E-PrintsUCM   E-Prints Complutense  

Autor(es)

Díaz Díaz, Jesús Ildefonso -  Bermejo, R. -  Carpio, Jaime -  Tello, J. Ignacio - 

Id.: 55287211

Idioma: español  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras claveAnálisis funcional y teoría de operadores - 

Tipo de recurso: info:eu-repo/semantics/article  -  PeerReviewed  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: info:eu-repo/semantics/embargoedAccess

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] http://eprints.ucm.es/15131/
[References] http://www.sciencedirect.com/science/article/pii/S0895717708001386
[References] http://dx.doi.org/10.1016/j.mcm.2008.04.010

Fecha de contribución: 18-oct-2016

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