ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Inverse Problem for Incomplete Sobolev Type Equation of Higher Order

Author(s):

Alyona Aleksandrovna Zamyshlyaeva

Director of the Institute of Natural Scinces and Mathematics,
Doctor of Sciences (Phys&Math), Professor
South Ural State University (National Research University) in Chelyabinsk

zamyshliaevaaa@susu.ru

Aleksandr Valeryevich Lut

Post graduate student,
Assistant of the Department of Applied Mathematics and Programming
South Ural State University (National Research University) in Chelyabinsk

lutav@susu.ru

Abstract:

The article is devoted to the study of the inverse problem for a high-order Sobolev type equation. Mathematical models based on such equations describe various problems of hydrodynamics and elasticity theory. The main result of the article is to find sufficient conditions for the existence and uniqueness of a solution to the original problem. At first using the theory of relatively bounded operators, the original problem is reduced to the equivalent system of two problems, which are usually called regular and singular. Thus, the solution to the original problem is represented as the sum of the solutions of these two problems. Further, the regular problem is reduced to a first-order equation. Then, by the method of successive approximations, the required smoothness for the function

Keywords

References:

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