%0 Journal Article
%A Díaz Díaz, Jesús Ildefonso
%A Bermejo, R.
%A Carpio, Jaime
%A Tello, J. Ignacio
%T Mathematical and numerical analysis of a nonlinear diffusive climate energy balance model
%D 2009
%@ 0895-7177
%U https://hdl.handle.net/20.500.14352/42167
%X 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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