The Carleman-based contraction principle to reconstruct the potential of nonlinear hyperbolic equations

2022/04/12 by Dinh-Liem Nguyen, Loc Nguyen, Nguyen, Dinh-Liem +3
Mathematics · Physics and Astronomy · #FOS: Mathematics #Mathematical Analysis and Transform Methods #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2204.06060

openalex publication_date 2022/04/12 · openalex created_date 2022/04/19 · openalex updated_date 2026/07/28

Abstract

We develop an efficient and convergent numerical method for solving the inverse problem of determining the potential of nonlinear hyperbolic equations from lateral Cauchy data. In our numerical method we construct a sequence of linear Cauchy problems whose corresponding solutions converge to a function that can be used to efficiently compute an approximate solution to the inverse problem of interest. The convergence analysis is established by combining the contraction principle and Carleman estimates. We numerically solve the linear Cauchy problems using a quasi-reversibility method. Numerical examples are presented to illustrate the efficiency of the method.

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