Carleman estimates and the contraction principle for an inverse source problem for nonlinear hyperbolic equations

DOI10.1088/1361-6420/AC4D09zbMath1483.35343arXiv2108.03500OpenAlexW4206350470WikidataQ115548128 ScholiaQ115548128MaRDI QIDQ5030167

Michael V. Klibanov, Loc Hoang Nguyen

Publication date: 16 February 2022

Published in: Inverse Problems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.03500

zbMATH Keywords

numerical methodscontraction principlenonlinear hyperbolic equationsCarleman estimateglobally convergent numerical method

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Initial value problems for second-order hyperbolic equations (35L15) Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs (65M32) Second-order semilinear hyperbolic equations (35L71)

Related Items (6)

Global reconstruction of initial conditions of nonlinear parabolic equations via the Carleman-contraction method ⋮ Reconstructing a space-dependent source term via the quasi-reversibility method ⋮ Simultaneous determination of the space-dependent source and initial value for a two-dimensional heat conduction equation ⋮ The Carleman contraction mapping method for quasilinear elliptic equations with over-determined boundary data ⋮ The Fourier-based dimensional reduction method for solving a nonlinear inverse heat conduction problem with limited boundary data ⋮ A Carleman-based numerical method for quasilinear elliptic equations with over-determined boundary data and applications

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