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 Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 11–20 (Mi semr893)

Differentical equations, dynamical systems and optimal control

On the Cauchy problem for matrix factorizations of the Helmholtz equation in a bounded domain

D. A. Juraev

Karshi State University, Karshi city, Kuchabog-17, 180100, Republic of Uzbekistan, Kashkadarya region

Abstract: In the paper it is considered the problem of regularization of the Cauchy problem for systems of elliptic type equations of the first order with constant coefficients factorisable Helmholtz operator in three-dimensional bounded domain. Using the results of [1–6], is constructed explicitly Carleman matrix and, based on the regularized solution of the Cauchy problem.

Keywords: The Cauchy problem, regularization, factorization, regular solution, fundamental solution.

DOI: https://doi.org/10.17377/semi.2018.15.002

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Bibliographic databases:

UDC: 517.946
MSC: 35J46
Received October 28, 2017, published January 12, 2018

Citation: D. A. Juraev, “On the Cauchy problem for matrix factorizations of the Helmholtz equation in a bounded domain”, Sib. Èlektron. Mat. Izv., 15 (2018), 11–20

Citation in format AMSBIB
\Bibitem{Jur18} \by D.~A.~Juraev \paper On the Cauchy problem for matrix factorizations of the Helmholtz equation in a bounded domain \jour Sib. \Elektron. Mat. Izv. \yr 2018 \vol 15 \pages 11--20 \mathnet{http://mi.mathnet.ru/semr893} \crossref{https://doi.org/10.17377/semi.2018.15.002} `