Publication: S-shaped bifurcation branch in a quasilinear multivalued model arising in climatology
Loading...
Files
Full text at PDC
Publication Date
1998-11-20
Advisors (or tutors)
Editors
Journal Title
Journal ISSN
Volume Title
Publisher
Elsevier
Citations
Exportar
Abstract
In this paper we show the existence of a continuous and unbounded connected S-shaped set {(Q, u)} where Q is the solar constant and u satisfies a quasilinear eventually multivalued stationary equation on a Riemannian manifold without boundary arising as a stationary energy balance model for the earth surface temperature.
Description
UCM subjects
Unesco subjects
Keywords
Citation
A. Ambrosetti, Critical points and nonlinear variational problems, Bull. Soc. Math. France, Memoire 49 (1992) [supplement].
A. Ambrosseti, M. Calahorrano, and F. Dobarro, Global branching for discontinuous problems, Comment. Math. Univ. Carolinae 31 (1990), 213–222.
D. Arcoya and M. Calahorrano, Multivalued non-positone problems, Rend. Mat. Accad. Lincei (9) 1 (1990), 117–123.
T. Aubin, "Nonlinear Analysis on Manifolds. Monge-Ampere Equations," Springer-Verlag, New York, 1982.
Ph. Benilan, M. G. Crandall, and P. Sachs, Some L 1 existence and dependence results for semilinear elliptic equations under nonlinear boundary conditions, Appl. Math. Optim. 17 (1988), 203–224.
H. Brezis, "Opérateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert," North-Holland, Amsterdam, 1973.
M. I. Budyko, The effects of solar radiation variations on the climate of the Earth, Tellus 21 (1969), 611–619.
J. I. Díaz, Mathematical analysis of some diffusive energy balance climate models, in "Mathematics, Climate and Environment" (J. I. Díaz and J. L. Lions, Eds.), pp. 28–56, Masson, Paris, 1993.
J. I. Díaz, J. Hernández, and L. Tello, On the multiplicity of equilibrium solutions to a nonlinear diffusion equation on a manifold arising in Climatology, J. Math. Anal. Appl. 216 (1997), 593–613.
J. I. Díaz and L. Tello, Sobre un modelo bidimensional en Climatología, in "Actas del XIII CEDYA/III Congreso de Matemática Aplicada" (A. Casal et al., Eds.), pp. 310–315, 1995.
J. I. Díaz and L. Tello, A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology, Collect. Math. (1998), to appear.
J. L. Gámez, Sub- and super-solutions in bifurcation problems, Nonlin. Anal. 28, No. 4 (1997), 625–632.
M. Ghil, Climate stability for a Sellers-type model, J. Atmos. Sci. 33 (1976), 3–20.
M. Ghil and S. Childress, "Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory and Climate Dynamics," Applied Mathematical Sciences, Vol. 60, Springer-Verlag, Berlin/New York, 1987.
G. Hetzer, The structure of the principal component for semilinear diffusion equations from energy balance climate models, Houston J. Math. 16 (1990), 203–216.
G. Hetzer, S-shapedness for energy balance climate models of Sellers type, in "The Mathematics of Models for Climatology and Environment" (J. I. Díaz, Ed.), pp. 253–288, Springer-Verlag, Heidelberg, 1996.
I. Massabo and C. A. Stuart, Elliptic eigenvalue problem with discontinuous nonlinearities, J. Math. Anal. Appl. 66 (1978), 261–281.
G. R. North, Multiple solutions in energy balance climate models, in "Paleogeography, Paleoclimatology, Paleoecology," Vol. 82, pp. 225–235, Elsevier, Amsterdam, 1990.
P. H. Rabinowitz, A global theorem for nonlinear eigenvalue problems and applications, in "Contributions to Nonlinear Functional Analysis" (E. H. Zarantonello, Ed.), pp. 11–36, Academic Press, New York, 1971.
W. D. Sellers, A global climatic model based on the energy balance of the earth-atmosphere system, J. Appl. Meteorol. 8 (1969), 392–400.
B. E. Schmidt, "Bifurcation of Stationary Solutions for Legendre-Type Boundary Value Problems Arising from Energy Balance Models," Thesis, Auburn University, 1994.
P. H. Stone, A simplified radiative-dynamical model for the static stability of rotating atmospheres, J. Atmos. Sci. 29, No. 3 (1972), 405–418.
G. T. Whyburn, "Topological Analysis," Princeton Univ. Press, Princeton, NJ, 1955.