RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
 General information Latest issue Archive Impact factor Search papers Search references RSS Latest issue Current issues Archive issues What is RSS

 Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki: Year: Volume: Issue: Page: Find

 Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2019, Volume 29, Issue 2, Pages 166–182 (Mi vuu674)

MATHEMATICS

Inverse boundary value problem for the linearized Benney-Luke equation with nonlocal conditions

Ya. T. Megralieva, B. K. Velievab

a Baku State University, ul. Z. Khalilova, 23, Baku, AZ1148, Azerbaijan
b Ganja State University, ul. Khatai, 187, Ganja, AZ2000, Azerbaijan

Abstract: The paper investigates the solvability of an inverse boundary-value problem with an unknown coefficient and the right-hand side, depending on the time variable, for the linearized Benney-Luke equation with non-self-adjoint boundary and additional integral conditions. The problem is considered in a rectangular domain. A definition of the classical solution of the problem is given. First, we consider an auxiliary inverse boundary-value problem and prove its equivalence (in a certain sense) to the original problem. To investigate the auxiliary inverse boundary-value problem, the method of separation of variables is used. By applying the formal scheme of the variable separation method, the solution of the direct boundary problem (for a given unknown function) is reduced to solving the problem with unknown coefficients. Then, the solution of the problem is reduced to solving a certain countable system of integro-differential equations for the unknown coefficients. In turn, the latter system of relatively unknown coefficients is written as a single integro-differential equation for the desired solution. Next, using the corresponding additional conditions of the inverse auxiliary boundary-value problem, to determine the unknown functions, we obtain a system of two nonlinear integral equations. Thus, the solution of an auxiliary inverse boundary-value problem is reduced to a system of three nonlinear integro-differential equations with respect to unknown functions. A special type of Banach space is constructed. Further, in a ball from a constructed Banach space, with the help of contracted mappings, we prove the solvability of a system of nonlinear integro-differential equations, which is also the unique solution to the auxiliary inverse boundary-value problem. Finally, using the equivalence of these problems the existence and uniqueness of the classical solution of the original problem are proved.

Keywords: inverse boundary value problem, Benney-Luke equation, existence, uniqueness of classical solution.

DOI: https://doi.org/10.20537/vm190203

Full text: PDF file (231 kB)
References: PDF file   HTML file

Bibliographic databases:

UDC: 517.95
MSC: 35-XX

Citation: Ya. T. Megraliev, B. K. Velieva, “Inverse boundary value problem for the linearized Benney-Luke equation with nonlocal conditions”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 29:2 (2019), 166–182

Citation in format AMSBIB
\Bibitem{MegVel19} \by Ya.~T.~Megraliev, B.~K.~Velieva \paper Inverse boundary value problem for the linearized Benney-Luke equation with nonlocal conditions \jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki \yr 2019 \vol 29 \issue 2 \pages 166--182 \mathnet{http://mi.mathnet.ru/vuu674} \crossref{https://doi.org/10.20537/vm190203} \elib{https://elibrary.ru/item.asp?id=39136242} 

• http://mi.mathnet.ru/eng/vuu674
• http://mi.mathnet.ru/eng/vuu/v29/i2/p166

 SHARE:

Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. L. I. Mammadova, I. M. Nabiev, “Spektralnye svoistva operatora Shturma–Liuvillya so spektralnym parametrom, kvadratichno vkhodyaschim v granichnoe uslovie”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:2 (2020), 237–248
•  Number of views: This page: 217 Full text: 114 References: 10