The Carleman-based contraction principle to reconstruct the potential of nonlinear hyperbolic equations. (15th December 2022)

• Record Type: Journal Article
• Authors: Nguyen, Dinh-Liem; Nguyen, Loc H.; Truong, Trung
• Is Part Of: Computers & mathematics with applications. Volume 128(2022)
• Page Start: 239
• Page End: 248
• Publication Date: 2022-12-15
• Subjects: Coefficient inverse problem -- Numerical reconstruction -- Carleman estimate -- Contraction principle -- Nonlinear hyperbolic equations; Electronic data processing -- Periodicals; Mathematics -- Data processing -- Periodicals; 510.28541
• DOI: 10.1016/j.camwa.2022.10.021
• Languages: English
• ISSNs: 0898-1221

Abstract

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.