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

Autor:	Dinh-Liem Nguyen, Loc H. Nguyen, Trung Truong
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	Computational Mathematics Computational Theory and Mathematics Modeling and Simulation FOS: Mathematics Numerical Analysis (math.NA) Mathematics - Numerical Analysis
Popis:	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. 18 pages
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4708831da0d5b8504fce3471aa4fb8b2 http://arxiv.org/abs/2204.06060 Zobrazit plný text záznamu