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
- inverse problem
- method of successive approximations
- relative boundedness of operator
- Sobolev type equation
References:
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