Determination of the insolation function in the nonlinear Sellers climate model
Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 5, p. 683-713

We are interested in the climate model introduced by Sellers in 1969 which takes the form of some nonlinear parabolic equation with a degenerate diffusion coefficient. We investigate here some inverse problem issue that consists in recovering the so-called insolation function. We not only solve the uniqueness question but also provide some strong stability result, more precisely unconditional Lipschitz stability in the spirit of the well-known result by Imanuvilov and Yamamoto (1998) [22]. The main novelties rely in the fact that the considered model is degenerate and above all nonlinear. Indeed we provide here one of the first result of Lipschitz stability in a nonlinear case.

DOI : https://doi.org/10.1016/j.anihpc.2012.03.003
Keywords: Nonlinear parabolic equation, Degenerate diffusion, Climate models, Inverse problems, Carleman estimates, Hardy inequalities
@article{AIHPC_2012__29_5_683_0,
     author = {Tort, J. and Vancostenoble, J.},
     title = {Determination of the insolation function in the nonlinear Sellers climate model},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {29},
     number = {5},
     year = {2012},
     pages = {683-713},
     doi = {10.1016/j.anihpc.2012.03.003},
     zbl = {1270.35283},
     mrnumber = {2971027},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2012__29_5_683_0}
}
Tort, J.; Vancostenoble, J. Determination of the insolation function in the nonlinear Sellers climate model. Annales de l'I.H.P. Analyse non linéaire, Volume 29 (2012) no. 5, pp. 683-713. doi : 10.1016/j.anihpc.2012.03.003. http://www.numdam.org/item/AIHPC_2012__29_5_683_0/

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