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Mathematical physics
Reconstruction of two functions in the model of vibrations of a string one end of which is placed in a moving medium
O. A. Andreyanovaa, A. Yu. Shcheglovb a Lomonosov Moscow State University, 119991, Moscow, Russia
b MSU-FPI University in Shenzhen, Longgang District, Dayunsirchen, 518172, Shenzhen, Guangdong, China
Abstract:
The paper considers an inverse problem of determining the coefficients in the model of small transverse vibrations of a homogeneous finite string one end of which is placed in a moving medium and the other is free. The vibrations are simulated by a hyperbolic equation on an interval. One boundary condition has a nonclassical form. Additional data for solving the inverse problem are the values of the solution of the forward problem with a known fixed value of the spatial argument. In the inverse problem, it is required to determine the function in the nonclassical boundary condition and a functional factor on the right-hand side of the equation. Uniqueness and existence theorems for the inverse problem are proved. For the forward problem, conditions for unique solvability are established in a form that simplifies the analysis of the inverse problem. For the numerical solution of the inverse problem, an algorithm is proposed for the stage-by-stage separate reconstruction of the sought-for functions using the method of successive approximations for integral equations.
Key words:
iterative algorithm, equation for vibrations, inverse problem.
Received: 05.08.2022 Revised: 23.10.2022 Accepted: 02.02.2023
Citation:
O. A. Andreyanova, A. Yu. Shcheglov, “Reconstruction of two functions in the model of vibrations of a string one end of which is placed in a moving medium”, Zh. Vychisl. Mat. Mat. Fiz., 63:5 (2023), 765–777; Comput. Math. Math. Phys., 63:5 (2023), 808–820
Linking options:
https://www.mathnet.ru/eng/zvmmf11554 https://www.mathnet.ru/eng/zvmmf/v63/i5/p765
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