Investigation of the Difference Problem for a Mixed Type Equation
Bakanov G.B. Meldebekova S.K.
July 2024Pleiades Publishing
Lobachevskii Journal of Mathematics
2024#45Issue 73246 - 3255 pp.
Abstract: In this article, we study the problem of recovering an unknown function based on its known integrals over a specified family of curves, with consideration given to a weight function. The main objective is to establish a methodology for solving the integral geometry problem by transforming it into a boundary value problem involving a second-order partial differential equation of mixed type. The obtained results provide valuable insights into the solution of the finite difference problem, which encompasses both the boundary and a certain neighborhood in its vicinity, taking into account the presence of specific types of singularities. The estimation theorem for the solution is proven using a specialized factor-based technique. The implications of these findings extend to diverse applications, notably in fields such as seismic and medical imaging, as well as non-destructive material characterization. By presenting a comprehensive analysis and a detailed exploration of the problem at hand, this study contributes to the advancement of the theory and practical implementation of integral geometry in various scientific and technological domains.
boundary value problem , discrete problem , ill-posed problems , quadratic form , stability estimate
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Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkestan, Kazakhstan
Khoja Akhmet Yassawi International Kazakh-Turkish University
10 лет помогаем публиковать статьи Международный издатель
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