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A criterion of solvability of the elliptic Cauchy problem in a multi-dimensional cylindrical domain

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Abstract
In this paper, we consider the Cauchy problem for multidimensional elliptic equations in a cylindrical domain. The method of spectral expansion in eigenfunctions of the Cauchy problem for equations with deviating argument establishes a criterion of the strong solvability of the considered elliptic Cauchy problem. It is shown that the ill-posedness of the elliptic Cauchy problem is equivalent to the existence of an isolated point of the continuous spectrum for a self-adjoint operator with deviating argument.
Keywords
Applied Mathematics, Analysis, Numerical Analysis, Computational Mathematics, Elliptic Cauchy problem, self-adjoint operator, elliptic operator with deviating argument, REGULARIZATION

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MLA
Kalmenov, Tynysbek Sh., et al. “A Criterion of Solvability of the Elliptic Cauchy Problem in a Multi-Dimensional Cylindrical Domain.” COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, vol. 64, no. 3, 2019, pp. 398–408, doi:10.1080/17476933.2018.1437423.
APA
Kalmenov, T. S., Sadybekov, M. A., & Torebek, B. (2019). A criterion of solvability of the elliptic Cauchy problem in a multi-dimensional cylindrical domain. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 64(3), 398–408. https://doi.org/10.1080/17476933.2018.1437423
Chicago author-date
Kalmenov, Tynysbek Sh., Makhmud A. Sadybekov, and Berikbol Torebek. 2019. “A Criterion of Solvability of the Elliptic Cauchy Problem in a Multi-Dimensional Cylindrical Domain.” COMPLEX VARIABLES AND ELLIPTIC EQUATIONS 64 (3): 398–408. https://doi.org/10.1080/17476933.2018.1437423.
Chicago author-date (all authors)
Kalmenov, Tynysbek Sh., Makhmud A. Sadybekov, and Berikbol Torebek. 2019. “A Criterion of Solvability of the Elliptic Cauchy Problem in a Multi-Dimensional Cylindrical Domain.” COMPLEX VARIABLES AND ELLIPTIC EQUATIONS 64 (3): 398–408. doi:10.1080/17476933.2018.1437423.
Vancouver
1.
Kalmenov TS, Sadybekov MA, Torebek B. A criterion of solvability of the elliptic Cauchy problem in a multi-dimensional cylindrical domain. COMPLEX VARIABLES AND ELLIPTIC EQUATIONS. 2019;64(3):398–408.
IEEE
[1]
T. S. Kalmenov, M. A. Sadybekov, and B. Torebek, “A criterion of solvability of the elliptic Cauchy problem in a multi-dimensional cylindrical domain,” COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, vol. 64, no. 3, pp. 398–408, 2019.
@article{8713840,
  abstract     = {{In this paper, we consider the Cauchy problem for multidimensional elliptic equations in a cylindrical domain. The method of spectral expansion in eigenfunctions of the Cauchy problem for equations with deviating argument establishes a criterion of the strong solvability of the considered elliptic Cauchy problem. It is shown that the ill-posedness of the elliptic Cauchy problem is equivalent to the existence of an isolated point of the continuous spectrum for a self-adjoint operator with deviating argument.}},
  author       = {{Kalmenov, Tynysbek Sh. and Sadybekov, Makhmud A. and Torebek, Berikbol}},
  issn         = {{1747-6933}},
  journal      = {{COMPLEX VARIABLES AND ELLIPTIC EQUATIONS}},
  keywords     = {{Applied Mathematics,Analysis,Numerical Analysis,Computational Mathematics,Elliptic Cauchy problem,self-adjoint operator,elliptic operator with deviating argument,REGULARIZATION}},
  language     = {{eng}},
  number       = {{3}},
  pages        = {{398--408}},
  title        = {{A criterion of solvability of the elliptic Cauchy problem in a multi-dimensional cylindrical domain}},
  url          = {{http://dx.doi.org/10.1080/17476933.2018.1437423}},
  volume       = {{64}},
  year         = {{2019}},
}

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