RT Journal Article
T1 Mathematical and numerical analysis of a nonlinear diffusive climate energy balance model
A1 Díaz Díaz, Jesús Ildefonso
A1 Bermejo, R.
A1 Carpio, Jaime
A1 Tello, J. Ignacio
AB 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.
PB Pergamon-Elsevier Science LTD
SN 0895-7177
YR 2009
FD 2009-03
LK https://hdl.handle.net/20.500.14352/42167
UL https://hdl.handle.net/20.500.14352/42167
LA spa
DS Docta Complutense
RD 7 jun 2025