Inverse Problem for the Sobolev Type Equation of Higher Order

Alyona Zamyshlyaeva and Aleksandr Lut
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Alyona Zamyshlyaeva: Department of Applied Mathematics and Programming, South Ural State University, 454080 Chelyabinsk, Russia
Aleksandr Lut: Department of Applied Mathematics and Programming, South Ural State University, 454080 Chelyabinsk, Russia

Mathematics, 2021, vol. 9, issue 14, 1-13

Abstract: 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.

Keywords: Sobolev type equation; inverse problem; high-order equation; method of successive approximations; polynomial boundedness of operator pencils (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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