On a climatological energy balance model with continents distribution

Arturo Hidalgo; Lourdes Tello

doi:10.3934/dcds.2015.35.1503

Article Contents

2015, Volume 35, Issue 4: 1503-1519. Doi: 10.3934/dcds.2015.35.1503

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On a climatological energy balance model with continents distribution

Arturo Hidalgo^1, and
Lourdes Tello^2,

1.
Dept. Matemática Aplicada y Métodos Informáticos. E.T.S.I. Minas y Energía, Universidad Politécnica de Madrid, Madrid, E-28003
2.
Dept. Matemática Aplicada. ETS Arquitectura, Universidad Politécnica de Madrid, Madrid, E-28040

Received: September 2013

Revised: May 2014

Published: May 2017

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Abstract

We present some results on the mathematical treatment of a global two-dimensional diffusive climate model with land - sea distribution. 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 surface with land - sea configuration. In the oceanic areas the model is coupled with a deep ocean model. The coupling is given by a dynamic and diffusive boundary condition. We study the existence of a bounded weak solution and its numerical approximation.

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Mathematics Subject Classification: Primary: 35K55, 65M08; Secondary: 35R01, 35K92, 35R70.

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