Inverse problem of reconstruction of degenerate diffusion coefficient in a parabolic equation. (2nd November 2021)

• Record Type: Journal Article
• Authors: Cannarsa, Piermarco; Doubova, Anna; Yamamoto, Masahiro
• Is Part Of: Inverse problems. Volume 37:Number 12(2021)
• Publication Date: 2021-11-02
• Subjects: inverse problems -- degenerate parabolic equations -- numerical reconstruction; Inverse problems (Differential equations) -- Periodicals; 515.357
• DOI: 10.1088/1361-6420/ac274b
• Languages: English
• ISSNs: 0266-5611

Abstract

Abstract: We consider the inverse problem of identification of degenerate diffusion coefficient of the form x α a ( x ) in a one dimensional parabolic equation by some extra data. We first prove by energy methods the uniqueness and Lipschitz stability results for the identification of a constant coefficient a and the power α by knowing interior data at some time. On the other hand, we obtain the uniqueness result for the identification of a general diffusion coefficients a ( x ) and also the power α form boundary data on one side of the space interval. The proof is based on global Carleman estimates for a hyperbolic problem and an inversion of the integral transform similar to the Laplace transform. Finally, the theoretical results are satisfactory verified by numerically experiments.