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 Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 1865–1877 (Mi semr1042)

Real, complex and functional analysis

On the Cauchy problem for matrix factorizations of the Helmholtz equation in an unbounded domain in ${\mathbb R}^{2}$

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 matrix factorisations of the Helmholtz equation in an unbounded planar domain. Using the Carleman matrix found an explicitly regularized solution of the Cauchy problem for matrix factorizations of the Helmholtz equation in two-dimensional unbounded domain.

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

DOI: https://doi.org/10.33048/semi.2018.15.151

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Bibliographic databases:

UDC: 517.946
MSC: 35J46
Received January 17, 2018, published December 31, 2018

Citation: D. A. Juraev, “On the Cauchy problem for matrix factorizations of the Helmholtz equation in an unbounded domain in ${\mathbb R}^{2}$”, Sib. Èlektron. Mat. Izv., 15 (2018), 1865–1877

Citation in format AMSBIB
\Bibitem{Jur18} \by D.~A.~Juraev \paper On the Cauchy problem for matrix factorizations of the Helmholtz equation in an unbounded domain in ${\mathbb R}^{2}$ \jour Sib. \Elektron. Mat. Izv. \yr 2018 \vol 15 \pages 1865--1877 \mathnet{http://mi.mathnet.ru/semr1042} \crossref{https://doi.org/10.33048/semi.2018.15.151} `