A criterion of solvability of the elliptic Cauchy problem in a multi-dimensional cylindrical domain
- Author
- Tynysbek Sh. Kalmenov, Makhmud A. Sadybekov and Berikbol Torebek (UGent)
- Organization
- 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
Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8713840
- 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. Sh., 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 TSh, 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. Sh. 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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