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.
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Funding
This work was supported in part by the National Natural Science Foundation of China (no. 12171036) and the Beijing Natural Science Foundation (Key Project no. Z210001).
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Translated by E. Chernokozhin
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Andreyanova, O.A., Shcheglov, A.Y. Reconstruction of Two Functions in the Model of Vibrations of a String One End of Which Is Placed in a Moving Medium. Comput. Math. and Math. Phys. 63, 808–820 (2023). https://doi.org/10.1134/S0965542523050032
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DOI: https://doi.org/10.1134/S0965542523050032