Publication: Infinitely many stationary solutions for a simple climate model via a shooting method
Full text at PDC
Tello del Castillo, Lourdes
Advisors (or tutors)
John Wiley & Sons Ltd.
In this paper, we study the number of steady solutions of a non-linear model arising in Climatology. By applying a shooting method we show the existence of infinitely many steady solutions for some values of a parameter (the solar constant). This method allows us to determine how many times a solution attains the critical temperature (-10degreesC) at which the coalbedo is assumed to be discontinuous.
Stone PH. A simplified radiative-dynamical model for the static stability of rotating atmospheres. Journal of Atmospheric Science 1972; 29(3):405–418. Díaz JI, Hernández J, Tello L. On the multiplicity of equilibrium solutions to a non-linear diffusion equation on a manifold arising in Climatology. Journal of Mathematical Analysis and Applications 1997; 216:593–613. Arcoya D, Díaz JI, Tello L. S-shaped bifurcation branch in a quasilinear multivalued model arising in Climatology. Journal of Differential Equations 1998; 150:215–225. Tello L. Tratamiento matemático de algunos modelos no lineales que aparecen en Climatología. Ph.D. Thesis, Univ. Complutense de Madrid, 1996. Hetzer G. S-shapedness for energy balance climate models of Sellers-type. In The Mathematics of models for Climatology and Environment, NATO ASI Series, Serie I: Global Environmental Change, vol. 48, Diaz JI (ed.). Springer: Berlin, 1997. Drazin PG, Griffel DH. On the branching structure of diffusive climatological models. Journal of Atmospheric Science 1977; 34:1969–1706. North GR. Introduction to simple climate model. In Mathematics, Climate and Environment, Diaz JI, Lions JL (eds). Masson: Paris, 1993. Schmidt BE. Bifurcation of stationary solutions for Legendre-type boundary value problems arising from climate modeling. PhD Thesis, Auburn Univ., 1994. Díaz JI, Tello L. A non-linear parabolic problem on a Riemannian manifold without boundary arising in Climatology. Collectanea Mathematica 1997; 50:19–51. Hetzer G. The number of stationary solutions for one-dimensional Budyko-type climate models, to appear in Nonlinear Analysis.