A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology
| dc.contributor.author | Díaz Díaz, Jesús Ildefonso | |
| dc.contributor.author | Tello, L. | |
| dc.date.accessioned | 2023-06-20T20:10:20Z | |
| dc.date.available | 2023-06-20T20:10:20Z | |
| dc.date.issued | 1999 | |
| dc.description.abstract | We present some results on the mathematical treatment of a global twodimensional diffusive climate model. The model is based on a long time averaged energy balance and leads to a nonlinear parabolic equation for the averaged surface temperature. The spatial domain is a compact two-dimensional Riemannian manifold without boundary simulating the Earth. We prove the existence of bounded weak solutions via a fixed point argument. Although, the uniqueness of solutions may fail, in general, we give a uniqueness criterion in terms of the behaviour of the solution near its “ice caps”. | |
| dc.description.department | Depto. de Análisis Matemático y Matemática Aplicada | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/33160 | |
| dc.identifier.issn | 0010-0757 | |
| dc.identifier.officialurl | http://collectanea.ub.edu/index.php/Collectanea/article/view/3958/4807 | |
| dc.identifier.relatedurl | http://collectanea.ub.edu/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/59742 | |
| dc.issue.number | 1 | |
| dc.journal.title | Collectanea Mathematica | |
| dc.language.iso | eng | |
| dc.page.final | 51 | |
| dc.page.initial | 19 | |
| dc.publisher | Universidad de Barcelona | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 517.9 | |
| dc.subject.ucm | Ecuaciones diferenciales | |
| dc.subject.unesco | 1202.07 Ecuaciones en Diferencias | |
| dc.title | A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology | |
| dc.type | journal article | |
| dc.volume.number | 50 | |
| dcterms.references | H.W. Alt and S. Luckhaus, Quasilinear Elliptic - Parabolic Differential Equations, Math. Z. 183 (1983), 311–341. T. Aubin, Nonlinear Analysis on Manifolds, Monge-Ampere Equations, Springer-Verlag, New York, 1982. V. Barbu, Nonlinear semigroups and differential equations in Banach spaces, Noordhooff International Publishing, 1976. Ph. Benilan, Evolution Equations and Accretive Operator, Lecture Notes, Univ. of Kentucky, 1981. Ph. Benilan, Equations d’evolution dans un espace de Banach quelconque et applications, These,Orsay 1972. R. Bermejo, Numerical solution to a two-dimensional diffusive climate model, In Modelado de Sistemas en Oceanografía, Climatología y Ciencias Medio - Ambientales: Aspectos Matemáticos y Numéricos , A. Valle and C. Parés eds., pp. 15-30, 1994. R. Bermejo, J.I. Díaz and L. Tello (1998), Article in preparation. W.M. Boothby, An Introduction to Differentiable Manifolds and Riemannnian Geometry, Academic Press, New York, 1975. H. Brezis, Operateurs maximaux monotones et semigroupes de contractions dans les espaces de Hilbert, North Holland, Amsterdam, 1973. H. Brezis, Analyse Fonctionelle, Masson, Paris, 1983. M.I. Budyko, The efects of solar radiation variations on the climate of the Earth, Tellus 21 (1969), 611–619. T. Cazenave and H. Haraux, Introduction aux problemes d’evolution semi-lineaires, Mathematiques et Applications, 1. Ed. Ellipses, Paris, 1990. I. Chavel, Eigenvalues in Riemannian Geometry, Academic J.I. Díaz, Nonlinear Partial Differential Equations and Free Boundaries, Pitman, Londres, 1985. J.I. Díaz, Elliptic and Parabolic Quasilinear Equations giving rise to a free boundary: the boundary of the support of the solutions, In Nonlinear Analysis and Applications, Proceedings of Symposia in Pure Mathematics, F.E. Browder ed. vol. 45, AMS, Rhode Island, pp. 381-393, 1986. J.I. Díaz, Mathematical Analysis of some diffusive energy balance climate models, In the book Mathematics, Climate and Environment, J.I. Díaz and J.L. Lions eds. Masson, Paris, pp. 28-56, 1993. J.I. Díaz and I.I. Vrabie, Existence for reaction diffusion systems, A compactness method approach, J. Math. Anal. Appl. 188(2) (1994), 521–328. E. Feireisl, A note on uniqueness for parabolic problems with discontinuous nonlinearities, Nonlinear Anal. 16 (1991), 1053–1056. E. Feireisl and J. Norbury, Some Existence, Uniqueness, and Nonuniqueness Theorems for solutions of Parabolic Equations with Discontinuous Nonlinearities, Proc. Royal. Soc. Edinburgh 119 A (1991), 1–17. S. Gallot, D. Hulin and J. Lafontaine, Riemannian Geometry, Springer-Verlag, 1987. M. Ghil and S. Childress, Topics in Geophysical Fluid Dynamics: Atmospheric Dynamics, Dynamo Theory and Climate Dynamics, Springer-Verlag, Applied Mathematical Sciences, 1987. R. Gianni and J. Hulshof, The semilinear heat equation with a Heaviside source term, European J. Appl. Math. 3 (1992), 367–379. I.M. Held and M.J. Suárez, Simple Albedo Feedback models of the icecaps, Tellus 36 1974. A. Henderson-Sellers and K. McGuffie, Introducción a los modelos climáticos, Omega, Barcelona,1990. G. Hetzer, The structure of the principal component for semilinear diffusion equations from energy balance climate models, Houston J. Math. 16 (1990), 203–216. O.A. Ladyzenskaya, V.A. Solonnikov and N.N. Ural‘ceva, Linear and Quasilinear Equations of Parabolic type, Transl. Math. Monographs, 23 Amer. Math. Soc, Providence, R. I, 1968. R.Q. Lin and G.R. North, A study of abrupt climate change in a simple nonlinear climate model, Climate Dynamics 4 (1990), 253–261. J.L. Lions, Quelques methodes de resolution des problemes aux limites non lineaires , Dunod. Paris, 1969. J.G. Mengel, D.A. Short and G.R. North, Seasonal snowline instability in an energy balance model, Climate Dynamics 2 (1988), 127–131. G.R. North, Multiple solutions in energy balance climate models, In Paleogeography, Paleoclimatology, Paleoecology (Global and Planetary Change Section), 82 225–235, Elsevier Science Publishers B.V. Amsterdam, 1990. G.R. North, L. Howard, D. Pollard and B. Wielicki, Variational formulation of Budyko – Sellers climate models, J. Atmospheric Sci. 36(2) (1979). C.V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Publishing Corporation, New York, 1992. M.H. Protter and H.F. Weinberger, Maximum principles in Differential Equations, Prenctice Hall, Englewood Cliffs, New Jersey, 1967. W.D. Sellers, A global climatic model based on the energy balance of the earth-atmosphere system, J. Appl. Meteorol. 8 (1969), 392–400. P.H. Stone, A Simplified Radiative-Dynamical Model for the Static Stability of Rotating Atmospheres, J. Atmospheric Sci. 29(3) (1972), 405–418. L. Tello, Tratamiento matemático de algunos modelos no lineales en Climatología, Tesis Doctoral, Universidad Complutense de Madrid, Julio 1996. I.I. Vrabie, Compactness methods for nonlinear evolutions, Pitman Longman, London, 1987. X. Xu, Existence and Regularity Theorems for a Free Boundary Problem Governing a Simple Climate Model, Appl. Anal. 42 (1991), 33–59. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 | |
| relation.isAuthorOfPublication.latestForDiscovery | 34ef57af-1f9d-4cf3-85a8-6a4171b23557 |
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