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

Patrick Martinez (1) , Jacques Tort (1) , Judith Vancostenoble (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: PDEs on manifolds; nonlinear parabolic equations; cli-; mate models; inverse problems; Carleman estimates

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Patrick Martinez, Jacques Tort, Judith Vancostenoble. Lipschitz stability for an inverse problem for the 2D-Sellers model on a manifold. Rivista di Matematica della Università di Parma, 2016, 7, pp.351-389. ⟨hal-01834728⟩