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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2018, Volume 22, Number 2, Pages 269–292 (Mi vsgtu1600)  

Differential Equations and Mathematical Physics

On the question of the correctness of inverse problems for the inhomogeneous Helmholtz equation

K. B. Sabitovab, N. V. Martem'yanovac

a Samara State Technical University, Samara, 443100, Russian Federation
b Samara State University of Social Sciences and Education, Samara, 443099, Russian Federation
c Samara National Research University, Samara, 443086, Russian Federation

Abstract: In the rectangular domain, the initial-boundary value problem for the Helmholtz equation and its non-local modifications are studied and the inverse problems for finding its right-hand side are studied. The solutions of direct problems with nonlocal boundary conditions and inverse problems are constructed in explicit form as the sums of orthogonal series in the system of eigenfunctions of the one-dimensional Sturm–Liouville spectral problem. The corresponding uniqueness theorems for the solution of all set problems are proved. Sufficient conditions for boundary functions are established, which are guaranteed by the existence and stability theorems for the solution of the proposed new problem statements.

Keywords: Helmholtz equation, initial-boundary value problem, nonlocal problems, inverse problems, uniqueness, existence, series, stability, integral equations

Funding Agency Grant Number
Russian Foundation for Basic Research 17-41-020516_р_а
16-31-00421_мол_а
This paper was written with the support of the Russian Foundation for Basic Research (grant no. 16–31–00421_mol_a), Russian Foundation for Basic Research and Republic Bashkortostan (grant no. 17–41–020516_r_a).


DOI: https://doi.org/10.14498/vsgtu1600

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Bibliographic databases:

Document Type: Article
UDC: 517.956.6
MSC: 35R30, 35M13
Received: January 10, 2018
Revised: April 21, 2018
Accepted: June 11, 2018
First online: June 27, 2018

Citation: K. B. Sabitov, N. V. Martem'yanova, “On the question of the correctness of inverse problems for the inhomogeneous Helmholtz equation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 22:2 (2018), 269–292

Citation in format AMSBIB
\Bibitem{SabMar18}
\by K.~B.~Sabitov, N.~V.~Martem'yanova
\paper On the question of the correctness of inverse problems
for~the~inhomogeneous Helmholtz equation
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2018
\vol 22
\issue 2
\pages 269--292
\mathnet{http://mi.mathnet.ru/vsgtu1600}
\crossref{https://doi.org/10.14498/vsgtu1600}
\zmath{https://zbmath.org/?q=an:07038286}
\elib{http://elibrary.ru/item.asp?id=35467731}


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  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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