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Article

Inverse Problem for the Sobolev Type Equation of Higher Order

Department of Applied Mathematics and Programming, South Ural State University, 454080 Chelyabinsk, Russia
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Author to whom correspondence should be addressed.
Academic Editor: Fasma Diele
Mathematics 2021, 9(14), 1647; https://doi.org/10.3390/math9141647
Received: 8 June 2021 / Revised: 7 July 2021 / Accepted: 9 July 2021 / Published: 13 July 2021
The article investigates the inverse problem for a complete, inhomogeneous, higher-order Sobolev type equation, together with the Cauchy and overdetermination conditions. This problem was reduced to two equivalent problems in the aggregate: regular and singular. For these problems, the theory of polynomially bounded operator pencils is used. The unknown coefficient of the original equation is restored using the method of successive approximations. The main result of this work is a theorem on the unique solvability of the original problem. This study continues and generalizes the authors’ previous research in this area. All the obtained results can be applied to the mathematical modeling of various processes and phenomena that fit the problem under study. View Full-Text
Keywords: Sobolev type equation; inverse problem; high-order equation; method of successive approximations; polynomial boundedness of operator pencils Sobolev type equation; inverse problem; high-order equation; method of successive approximations; polynomial boundedness of operator pencils
MDPI and ACS Style

Zamyshlyaeva, A.; Lut, A. Inverse Problem for the Sobolev Type Equation of Higher Order. Mathematics 2021, 9, 1647. https://doi.org/10.3390/math9141647

AMA Style

Zamyshlyaeva A, Lut A. Inverse Problem for the Sobolev Type Equation of Higher Order. Mathematics. 2021; 9(14):1647. https://doi.org/10.3390/math9141647

Chicago/Turabian Style

Zamyshlyaeva, Alyona, and Aleksandr Lut. 2021. "Inverse Problem for the Sobolev Type Equation of Higher Order" Mathematics 9, no. 14: 1647. https://doi.org/10.3390/math9141647

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