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Parameter Determination for Energy Balance Models with Memory

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Book cover Mathematical Approach to Climate Change and its Impacts

Part of the book series: Springer INdAM Series ((SINDAMS,volume 38))

Abstract

In this paper, we study two Energy Balance Models with Memory arising in climate dynamics, which consist in a 1D degenerate nonlinear parabolic equation involving a memory term, and possibly a set-valued reaction term (of Sellers type and of Budyko type, in the usual terminology). We provide existence and regularity results, and obtain uniqueness and stability estimates that are useful for the determination of the insolation function in Sellers’ model with memory.

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Acknowledgements

This research was partly supported by Istituto Nazionale di Alta Matematica through the European Research Group GDRE CONEDP. The authors acknowledge the MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata, CUP E83C18000100006. The authors also wish to thank K. Fraedrich for a very interesting discussion on the question of Energy Balance Models with Memory, and M. Ghil for inspiring remarks.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Roma “Tor Vergata”, Roma, Italy

    Piermarco Cannarsa & Martina Malfitana

  2. Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, CNRS UPS IMT, Toulouse, France

    Patrick Martinez

Authors
  1. Piermarco Cannarsa
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  2. Martina Malfitana
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  3. Patrick Martinez
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Correspondence to Piermarco Cannarsa .

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Editors and Affiliations

  1. Department of Mathematics, University of Rome "Tor Vergata", Rome, Italy

    Piermarco Cannarsa

  2. Istituto per le Applicazioni del Calcolo ‘M. Picone’, CNR, Rome, Italy

    Daniela Mansutti

  3. Institute of Geosciences & Earth Resources (IGG), National Research Council (CNR), Pisa, Italy

    Antonello Provenzale

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Cannarsa, P., Malfitana, M., Martinez, P. (2020). Parameter Determination for Energy Balance Models with Memory. In: Cannarsa, P., Mansutti, D., Provenzale, A. (eds) Mathematical Approach to Climate Change and its Impacts. Springer INdAM Series, vol 38. Springer, Cham. https://doi.org/10.1007/978-3-030-38669-6_2

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