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An energy balance climate model with hysteresis

Díaz Díaz, Jesús Ildefonso and Hetzer, G. and Tello del Castillo, Lourdes (2006) An energy balance climate model with hysteresis. Nonlinear analysis : theory, methods and applications, 64 (9). pp. 2053-2074. ISSN 0362-546X

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Abstract

Energy balance climate models of Budyko type lead to reaction-diffusion equations with slow diffusion and memory on the 2-sphere. The reaction part exhibits a jump discontinuity (at the snow line). Here we introduce a Babuska-Duhem hysteresis in order to account for a frequent repetition of sudden and fast warming followed by much slower cooling as observed from paleoclimate proxy data. Existence of global solutions and of a trajectory attractor will be established for the resulting system of a parabolic differential inclusion and an ode.

Item Type:Article
Uncontrolled Keywords:equations
Subjects:Sciences > Mathematics > Differential equations
ID Code:15405
References:

H. Amann, Linear and Quasilinear Problems, vol. 1, Abstract Linear Theory, Monographs in Mathematics, vol. 89, Birkhäuser, Basel-Boston-Berlin, 1995.

J.-P. Aubin, H. Frankowska, Set-valued analysis, Systems & Control: Foundations and Analysis, vol. 2, Birkhäuser, Boston-Basel-Berlin, 1990.

J.-P. Aubin, A. Cellina, Differential Inclusions, Grundlehren der mathematischen Wissenschaften, vol. 264, Springer, Berlin-Heidelberg-New York-Tokyo, 1984.

T. Aubin, Nonlinear Analysis on Manifolds. Monge-Ampère Equations, Springer, New York, 1982.

K. Bhattacharya, M. Ghil, I.L. Vulis, Internal variability of an energy balance climate model, J. Atmos. Sci. 39 (1982) 1747–1773.

H. Brezis, Opérateurs Maximaux Monotones et Semi-groupes de Contractions Dans un Espace de Hilbert, North-Holland, Amsterdam, 1973.

M. Brokate, J. Sprekels, Hysteresis and phase transition, Applied Mathematical Sciences, vol. 121, Springer, New York, 1996.

M.I. Budyko, The effect of solar radiation variations on the climate of the earth, Tellus 21 (1969) 611–619.

V.V. Chepyzhov, M.I. Vishik, Trajectory Attractors for the 2D Navier-Stokes system and some generalizations. Topol. Meth. Nonlinear Anal. 8 (1996) 217–243.

V.V. Chepyzhov, M.I. Vishik, Evolution equations and their trajectory attractors, J. Math. Pures Appl. 76 (1997) 913–964.

V.V. Chepyzhov, M.I. Vishik, Attractors for Equations of Mathematical Physics, vol. 49, American Mathematical Society, Colloquium Publications, 2002.

K. Deimling, Multivalued differential equations, De Gruyter series in nonlinear analysis and applications. vol. 1, de Gruyter, Berlin-New York, 1992.

J.I. Díaz, Mathematical analysis of some diffusive energy balance models, in: J.I. Díaz, J.L. Lions (Eds.), Mathematics, Climate and Environment, Mason, Paris, 1993, pp. 28–56.

J.I. Díaz (Ed.), The mathematics of models for climatology and environment, NATO ASI Series I: Global Environmental Changes, vol. 48, Springer, Berlin-Heidelberg-New York-Tokyo, 1997.

J.I. Díaz, J. Hernández, 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, G. Hetzer, A quasilinear functional reaction-diffusion equation arising in climatology, in Equations aux dérivées partielles et applications, Articles dédiés á J.-L. Lions, Gauthier-Villars, 1998, pp. 461–480.

E. DiBenedetto, Degenerate Parabolic Equations, Springer, New York-Berlin-Heidelberg, 1993.

J.I. Díaz, L. Tello, A nonlinear parabolic problem on a Riemannian manifold without boundary arising in Climatology, Collect. Math. 50 (1999) 19–51.

M. Ghil, S. Childress, Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory and Climate Dynamics, Applied Mathematical Sciences, Springer, Berlin, 1987.

J.K. Hale, Asymptotic Behavior of Dissipative Systems, American Mathematical Society, Providence, RI, 1988.

A. Henderson-Sellers, K.A. McGuffie, A Climate Modelling Primer, Wiley, New York, Chichester, 1987.

G. Hetzer, The shift-semiflow of a multi-valued evolution equation from climate modeling, Nonl. Anal. 47 (2001) 2905–2916.

G. Hetzer, A functional reaction-diffusion equation from climate modeling: S-shapedness of the principal branch, Differential Integral Equations 8 (1995) 1047–1059.

G. Hetzer, Global existence, uniqueness and continuous dependence for a reaction-diffusion equation with memory, European Journal of Differential Equations 1996 (1996) 1–16.

G. Hetzer, P.G. Schmidt, Analysis of energy balance models, in: V. Lakshmikantham (Ed.), World Congress of Nonlinear Analysts '92, Walter de Gruyter, Berlin, New York, 1996, pp. 1609–1618.

G. Hetzer, L. Tello, On a reaction-diffusion system arising in climatology, Dynamic Syst. Appl. 11 (2002) 381–402.

M.A. Krasnosel'skii, A.V. Pokrovskii, Systems with Hysteresis, Springer, Berlin, 1989.

I.D. Mayergoyz, Mathematical Models of Hysteresis, Springer, Berlin, 1993.

A.M. Meirmanov, The Stefan Problem, Walter de Gruyter, Berlin, New York, 1992.

J.A. Rial, Abrupt climate change: chaos and order at orbital and millennial scales, Global Planet. Change 41 (2004) 95–109.

G.R. Sell, Global attractors for the three-dimensional Navier-Stokes equations, J. Dynam. Differential Equations 8 (1996) 1–33.

G.R. Sell, Y. You, Dynamics of evolutionary equations, Applied Mathematical Sciences, vol. 143, Springer, New York, 2002.

W.B. Sellers, A global climate model based on the energy balance of the Earth-atmosphere system, J. Appl. Meteor. 8 (1969) 301–320.

R.E. Showalter, T.D. Little, U. Hornung, Parabolic with hysteresis. Distributed parameter systems: modelling and control (Warsaw, 1995), Control Cybernet. 25 (3) (1996) 631–643.

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

A. Visintin, Differential Models of Hysteresis, Springer, Berlin, 1994.

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

A. Visintin (Ed.), Models of hysteresis, Pitman Research Notes in Mathematics, vol. 286, 1993.

J. Wu, Theory and Applications of Partial Functional Differential Equations, Applied Mathematical Sciences, vol. 119, Springer, New York-Berlin-Heidelberg, 1996.

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