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Mathematics > Numerical Analysis

arXiv:2302.12474 (math)
[Submitted on 24 Feb 2023 (v1), last revised 16 Mar 2023 (this version, v2)]

Title:Convexification for the Viscocity Solution for a Coefficient Inverse Problem for the Radiative Transfer Equation

Authors:Michael V. Klibanov, Jingzhi Li, Zhipeng Yang
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Abstract:A Coefficient Inverse Problem for the radiative transport equation is considered. The globally convergent numerical method, the so-called convexification, is developed. For the first time, the viscosity solution is considered for a boundary value problem for the resulting system of two coupled partial differential equations. A Lipschitz stability estimate is proved for this boundary value problem using a Carleman estimate for the Laplace operator. Next, the global convergence analysis is provided via that Carleman estimate. Results of numerical experiments demonstrate a high computational efficiency of this approach.
Subjects: Numerical Analysis (math.NA)
Cite as: arXiv:2302.12474 [math.NA]
  (or arXiv:2302.12474v2 [math.NA] for this version)
  https://doi.org/10.48550/arXiv.2302.12474

Submission history

From: Michael V. Klibanov [view email]
[v1] Fri, 24 Feb 2023 06:18:28 UTC (1,961 KB)
[v2] Thu, 16 Mar 2023 03:46:09 UTC (3,117 KB)
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