Riv. Mat. Univ. Parma, Vol. 7, No. 2, 2016

Patrick Martinez[a], Jacques Tort[b] and Judith Vancostenoble[c]

Lipschitz stability for an inverse problem for the 2D-Sellers model on a manifold

Pages: 351-389
Received: 11 February 2016
Accepted: 24 January 2017
Mathematics Subject Classification (2010): 58J35, 35K55.
Keywords: PDEs on manifolds, nonlinear parabolic equations, climate models, inverse problems, Carleman estimates.
Author address:
[a], [b], [c]: University of Toulouse 3, 118 route de Narbonne 31062 Toulouse Cedex 9, France

Abstract: In this paper, we are interested in some inverse problem that consists in recovering the so-called insolation function in the 2-D Sellers model on a Riemannian manifold that materializes the Earth's surface. For this nonlinear problem, we obtain a Lipschitz stability result in the spirit of the result by Imanuvilov-Yamamoto in the case of the determination of the source term in the linear heat equation. The paper complements an analogous study by Tort-Vancostenoble in the case of the 1-D Sellers model.

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