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On the multiplicity of equilibrium solutions to a nonlinear diffusion equation on a manifold arising in climatology

Díaz Díaz, Jesús Ildefonso and Hernández , J. and Tello del Castillo, José Ignacio (1997) On the multiplicity of equilibrium solutions to a nonlinear diffusion equation on a manifold arising in climatology. Journal of Mathematical Analysis and Applications, 216 (2). pp. 593-617. ISSN 0022-247X

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Abstract

We analyze the sensitivity of a climatological model with respect to small changes in one of the distinguished parameters: the solar constant. We start by proving the stabilization of solutions of the evolution model when time tends to infinity. Later, we study the stationary problem and obtain uniqueness or a multiplicity of solutions for different Values of the solar constant.

Item Type:Article
Uncontrolled Keywords:positive solutions; compact manifolds; models
Subjects:Sciences > Physics > Geophysics
ID Code:15727
References:

H. W. Alt and S. Luckhaus, Quasilinear elliptic-parabolic differential equations, Math. Z.183 (1983)., 311-341.

H. Amann, Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev.18(1976),620-709.

D. Arcoya, J. I. Díaz, and L. Tello, S-shaped bifurcation branch in a model arising in climatology, 1997 (submitted).

T. Aubin, ‘‘Nonlinear Analysis on Manifolds: Monge-Ampère Equations,’’ Springer Verlag, New York, 1982.

Ph. Benilan, M. G. Crandall, and P. Sachs, Some L1 existence and dependence results for semilinear elliptic equations under nonlinear boundary conditions, Appl. Math. Optim. 17 (1988), 203-224.

H. Brezis, Proprietés régularisantes de certains semi-groupes nonlinéaires, Israel J. Math. 9 (1971), 513-534.

H. Brezis, ‘‘Opérateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert,’’ North Holland, Amsterdam, 1973.

8. H. Brezis and L. Nirenberg, H1 versus C1 local minimizers, C. R. Acad. Sci. Paris, Série I 317 (1993), 465-472.

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 and L. Tello, Sobre un modelo bidimensional en Climatología, in ‘‘Actas del, XIII CEDYArIII 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. Collectanea Mathematica, 1997 (to appear).

J. I. Díaz and F. de Thélin, On a nonlinear parabolic problem arising in some models related to turbulent flows, SIAM J. Math. Anal. 25 (1994), 1085-1111.

J. Hernández, Qualitative methods for nonlinear diffusion equations, in ‘‘Nonlinear Diffusion Equations,’’ Lecture Notes, (A. Fasano and M. Primicerio, Eds.), pp. 47-118,

Springer Verlag, New York, 1986.

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,NATO ASI Series I: Global Environmental Change, No. 48, Springer Verlag, Heidelberg,1996.

M. Nakao, A difference inequality and its application to nonlinear evolution equations, J. Math. Soc. Japan 30 (1978), 747-762.

G. R. North, Introduction to simple climate models, in ‘‘Mathematics, Climate and Environment (J. I. Díaz and J. L. Lions, Eds.), pp. 139-159, Masson, Paris, 1993.

T. Ouyang, On the positive solutions of semilinear equations Duqluqhu ps0 on compact manifolds, Trans. Amer. Math. Soc. 331 (1992), 503-527.

T. Ouyang, On the positive solutions of semilinear equations Duqluqhu ps0 on compact manifolds, part II, Indiana Univ. Math. J. 40 (1991), 1083-1141.

W. D. Sellers, A global climatic model based on the energy balance of the earth-atmosphere system, J. Appl. Meteorol. 8 (1969), 392-400.

J. Simon, Compact sets in the space L p(0, T; B), Annali Mat. Pura Appl. CXLVI (1987), 65-96.

P. H. Stone, A simplified radiative-dynamical model for the static stability of rotating atmospheres, J. Atmospheric Sci. 29 (1972), 405-418.

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