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Zh. Vychisl. Mat. Mat. Fiz., 2019, Volume 59, Number 4, Pages 587–596 (Mi zvmmf10877)  

Existence of a solution of the inverse coefficient problem for a quasilinear hyperbolic equation

A. M. Denisov

Lomonosov Moscow State University, Moscow, 119992 Russia

Abstract: A problem with data on the characteristics for a quasilinear hyperbolic equation is considered. An inverse problem consisting in determining the unknown coefficient of the equation, depending on its solution, is formulated. As additional information for the inverse problem, the values of the solution of the problem with the data on the characteristics at a fixed value of one of the independent variables are specified. The existence theorem for the inverse problem is proved. The proof is based on deriving a nonlinear operator equation for the unknown coefficient and the proof of its solvability.

Key words: quasilinear hyperbolic equation, problem with data on characteristics, inverse problem, existence theorem, nonlinear operator equation.

Funding Agency Grant Number
Russian Foundation for Basic Research 17-01-00525_а
This work was supported in part by the Russian Foundation for Basic Research, project no. 17-01-00525.


DOI: https://doi.org/10.1134/S0044466919040021


English version:
Computational Mathematics and Mathematical Physics, 2019, 59:4, 550–558

Bibliographic databases:

UDC: 517.958
Received: 10.10.2018
Revised: 14.11.2018
Accepted:14.11.2018

Citation: A. M. Denisov, “Existence of a solution of the inverse coefficient problem for a quasilinear hyperbolic equation”, Zh. Vychisl. Mat. Mat. Fiz., 59:4 (2019), 587–596; Comput. Math. Math. Phys., 59:4 (2019), 550–558

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