Abstract
Climate models are distinguished by the relative importance they attach to the different components and processes of the climate system. One finds the so-called energy balance climate models at the bottom on a scale of models of increasing complexity, and coupled general circulation models of atmosphere and oceans at the top on that scale.
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References
Amann H (1976) Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. Siam Review 45:620–709
Amann H (1983) Dual semigroups and second order linear elliptic differential equations. Israel J. Math. 45:225–254
Amann H (1984) Existence and regularity for semilinear parabolic evolution equations. Ann. Scuola Norm. Sup. Pisa 11:593–676
Amann H (1990) Ordinary differential equations: an introduction to nonlinear analysis. de Gruyter, Berlin, New York
Amann H (1993) Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems in Function Spaces, Differential Operators and Nonlinear Analysis, Schmeisser H. D., Triebel H. (eds.) Teubner-Texte zur Mathematik 133:9–126
Bhattacharya K, Ghil M, Vulis IL (1982) Internal variability of an energy balance climate model. J. Atmosph. Sci. 39:1747–1773
Budyko MI (1969) The effect of solar radiation variations on the climate of the earth. Tellus 21:611–619
Daners D, Koch Medina P (1993) Abstract evolution equations, periodic problems and applications. Pitman Research Notes in Mathematics vol. 78
Diaz IJ (1995), this volume
Ghil M, Childress S (1987) Topics in geophysical fluid dynamics: atmospheric dynamics, dynamo theory, and climate dynamics. Springer-Verlag New York
Hale JK (1988) Asymptotic Behavior of Dissipative Systems. American Mathematical Society, Providence
Henderson-Sellers A, McGuffie K (1987) A Climate Modelling Primer.John Wiley and Sons Chichester
Hess P (1991) Periodic-parabolic boundary value problems and positivity. Pitman Research Notes in Mathematics vol 247
Hess P, Poláčik P (1993) Boundedness of prime periods of stable cycles and convergence to fixed points in discrete monotone dynamical systems. SIAM Journ. Math. Anal. 24:1312–1330
Hetzer G (1990) The structure of the principal component for semilinear diffusion equations from energy balance climate models. Houston J. Math. 16:203–216
Hetzer G (1994) 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 and Integral Equations 7:1419–1425
Hetzer G (1995) A functional reaction-diffusion equation from climate modeling: S-shapedness of the principal branch. Diff. and Integral Eq., to appear
Hetzer G,Jarausch H, Mackens W (1989) A multiparameter sensitivity analysis of a 2D diffusive climate model. Impact Comput. Sci. Eng. 1:327–393
Hetzer G, Schmidt PL (1990) A global attractor and stationary solutions for a reaction diffusion system arising from climate modeling. Nonlinear Analysis: Theory, Methods, and Appl. 14:915–926
Hetzer G, Schmidt PL (1992) Global existence and asymptotic behavior for a quasilinear reaction-diffusion system from climate modeling. J.Math. Anal. Appl. 160:250–262
Hetzer G, Schmidt PL (1995) Analysis of energy balance models. Proc. 1st World Congress of Nonlinear Analysts, to appear
Hirsch MW (1988) Stability and convergence in strongly monotone dynamical systems. J. Reine Angew. Math. 383:1–53
Kerscher W, Nagel R (1984) Asymptotic behavior of one-parameter semigroups of positive operators. Acta Applicandae Mathematicae 2:297–308
Lions JL, Temam R, Wang Shouhong (1992a) New formulation of the primitive equations of atmosphere and application. Nonlinearity 5:237–288
Lions JL, Temam R, Wang Shouhong (1992b) On the equation of the large-scale ocean. Nonlinearity 5:1007–1053
Lions JL, Temam R, Wang Shouhong (1992c) Models of the coupled atmosphere and ocean (CAO 1). Preprint, The Institute for Applied Mathematics and Scientific Computing 9206:1–52
Martin RH Jr., Smith HL (1990) Abstract functional differential equations and reaction-diffusion systems. Trans. Amer. Math. Soc. 321:1–44
Mora X (1983) Semilinear parabolic problems define semiflows on Ck spaces. Trans. AMS 278:21–55
North GR (1995), this volume
North GR, Calahan RE, Coakley JA (1981) Energy balance climate models. Review of Geophysics and Space Physics 19:91–121
North GR, Mengel JG, Short BA (1983) Simple energy balance models resolving the seasons and the continents: Applications to the astronomical theory of ice ages J. Geophys. Res. 88:6576–6586
Parrott ME (1989) Positivity and a principle of linearized stability for delay-differential equations. Diff. and Integral Eqns. 2: 170–182
Poláčik P, Tereščák I (1991) Convergence of cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems. Arch. Rat. Mech. Anal. 116:339–360
Schmidt BE (1994) Bifurcation of stationary solutions for Legendre type boundary value problems arising from energy balance models. Dissertation Auburn
Sellers WB (1969) A global climate model based on the energy balance of the earth-atmospere system. J. Appl. Meteor. 8:301–320
Shen W, Yi Y (1995) paper in preparation
Stewart HB (1974) Generation of analytic semigroups by strongly elliptic operators. Trans. AMS 259:299–310
Takáč P (1992) Domains of attraction of generic ω-imit sets for strongly monotone time-discrete semigroups. Journal reine angew. Math. 423:101–173
Wang Shouhong (1990/91) Approximate inertial manifolds for the 2D model of atmosphere. Numer. Funct. Anal, and Optimiz. 11:1043–1070
Wang Shouhong (1992a) On the 2D model of large-scale atmospheric motion: well-posedness and attractors. Nonlinear Analysis: Theory, Methods and Appl. 18:17–60
Wang Shouhong (1992b) Attractors for the 3D baroclinic quasi-geostrophic equations of large-scale atmosphere. J. Math. Anal. Appl. 165:266–283
Washington WM, Parkinson CL(1986) An introduction to three-dimensional climate modeling. University Science Books Mill Valley, CA
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Hetzer, G. (1997). S-shapedness for energy balance climate models of Sellers-Type. In: Díaz, J.I. (eds) The Mathematics of Models for Climatology and Environment. NATO ASI Series, vol 48. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-60603-8_7
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DOI: https://doi.org/10.1007/978-3-642-60603-8_7
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