Parameter Determination for Energy Balance Models with Memory

  • Piermarco CannarsaEmail author
  • Martina Malfitana
  • Patrick Martinez
Part of the Springer INdAM Series book series (SINDAMS, volume 38)


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.


Parameter determination Energy balance models Degenerate Parabolic equations 



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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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Piermarco Cannarsa
    • 1
    Email author
  • Martina Malfitana
    • 1
  • Patrick Martinez
    • 2
  1. 1.Dipartimento di MatematicaUniversità di Roma “Tor Vergata”RomaItaly
  2. 2.Institut de Mathématiques de Toulouse, UMR 5219Université de Toulouse, CNRS UPS IMTToulouseFrance

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