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Time periodic solutions for a diffusive energy balance model in climatology

Díaz Díaz, Jesús Ildefonso and Badii, M (1999) Time periodic solutions for a diffusive energy balance model in climatology. Journal of Mathematical Analysisand applications, 233 (2). pp. 713-729. ISSN 0022-247X

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We prove the existence of a periodic solution to the problem u(t) - Delta(p)u + R-e(x,u) is an element of mu Q(x,t)beta(u) in M x R, assumed p greater than or equal to 2, M a compact connected and oriented bidimensional Riemannian manifold without boundary, beta(u) a bounded maximal monotone graph (the coalbedo), Q(x, t) a time periodic function (the incoming solar radiation flux) and R-e a time independent strictly increasing function of the surface temperature u (the Earth emitted energy)

Item Type:Article
Uncontrolled Keywords:nonlinear parabolic equations; periodic solutions; supersolution; subsolution; Riemannian manifold
Subjects:Sciences > Mathematics > Differential equations
ID Code:15647

D. Arcoya, J. L. Díaz, and L. Tello, ‘‘S-shaped bifurcation branch in a model arising in climatology,’’ J. Differential Equations, 150 ,1998., 215-225.

T. Aubin, ‘‘Nonlinear Analysis on Manifold. Monge-Ampere Equations,’’ Springer-Verlag, Berlin, New York, 1982.

V. Barbu, ‘‘Nonlinear Semigroups and Differential Equations in Banach Spaces,’’ Noordhooff International Publishing, 1976.

Ph. Benilan, Operateurs accr´etifs et semi-groupes dans les espaces L p _1FpF`., in ‘‘Functional Analysis and Numerical Analysis,’’ ,H. Fujita, ed.. Japan Society for the

Promotion of Sciences, Tokyo, pp. 15-53, 1978.

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

M. I. Budyko, The effect of solar radiation variations on the climate of the Earth, Tellus, 21 ,1969., 611-619.

E. Di Benedetto, ‘‘Degenerate Parabolic Equations,’’ Springer-Verlag, Berlin, New York, 1993.

J. I. Díaz, ‘‘Nonlinear partial differential equations and free boundaries,’’ Pitman, London, 1985.

J. I. Díaz, Mathematical analysis of some diffusive energy balance models in climatology, 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, 1998., 593-613.

J. I. Díaz and M. A. Herrero, Estimates of the support of the solutions of some nonlinear elliptic and parabolic equations, Proc. Roy. Soc. Edinburgh Sect. A, 89A,1981., 249-258.

J. I. Díaz and L. Tello, A Nonlinear Parabolic Problem on a Riemannian Manifold Without Boundary Arising in Climatology, to appear in Collect. Math.,

G. Hetzer, Forced periodic oscillations in the climate system via an energy balance model, Comment. Math. Uni¨. Carolin. 28 ,1987., 593-401.

G. Hetzer, A parameter dependent time-periodic reaction-diffusion equation from climate modeling; S-shapedness of the principal branch of fixed points of the time 1-map,

Differential Integral Equations, 7 ,1994., 1419-1425.

C. V. Pao, ‘‘Nonlinear Parabolic and Elliptic Equations,’’ Plenum, New York, 1992.

P. H. Rabinowitz, Some global results for nonlinear eigenvalue problem, J. Funct. Anal.,7 ,1971., 487-513.

W. P. Sellers, A global climate model based on the energy balance of the Earth-atmo-sphere system, J. Appl. Meteorol., 8,1969., 392-400.

J. Simon, Compact sets in the space L p_0, T; B., Ann. Mat. Pura Appl. 146 ,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.

L. Tello, Tratamiento matematico de algunos modelos no lineales en Climatologia,Thesis, Universidad Complutense de Madrid, June 1996.

I. I. Vrabie, ‘‘Compactness Methods for Nonlinear Evolutions,’’ Pitman-Longman, London, 1987.

G. T. Whyburn, ‘‘Topological Analysis,’’ Princeton Univ. Press, Princeton, 1955.

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