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Article

Solution of the Ill-Posed Cauchy Problem for Systems of Elliptic Type of the First Order

by 1,2,†, 3,† and 4,*,†
1
Chair of Natural Science Disciplines, Higher Military Aviation School of the Republic of Uzbekistan, Karshi 180100, Uzbekistan
2
Department of Mathematics, Anand International College of Engineering, Jaipur 303012, India
3
Department of Mathematics, Faculty of Sciences, University of Maragheh, Maragheh 83111-55181, Iran
4
Department of Mathematics, Technical University of Cluj-Napoca, 28 Memorandumului Street, 400114 Cluj-Napoca, Romania
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editors: Sotiris K. Ntouyas, Bashir Ahmad and Jessada Tariboon
Fractal Fract. 2022, 6(7), 358; https://doi.org/10.3390/fractalfract6070358
Received: 8 May 2022 / Revised: 15 June 2022 / Accepted: 23 June 2022 / Published: 26 June 2022
(This article belongs to the Special Issue Initial and Boundary Value Problems for Differential Equations)
We study, in this paper, the Cauchy problem for matrix factorizations of the Helmholtz equation in the space Rm. Based on the constructed Carleman matrix, we find an explicit form of the approximate solution of this problem and prove the stability of the solutions. View Full-Text
Keywords: Carleman matrix; stability of the Cauchy problem; regularized solution; approximate solution Carleman matrix; stability of the Cauchy problem; regularized solution; approximate solution
MDPI and ACS Style

Juraev, D.A.; Shokri, A.; Marian, D. Solution of the Ill-Posed Cauchy Problem for Systems of Elliptic Type of the First Order. Fractal Fract. 2022, 6, 358. https://doi.org/10.3390/fractalfract6070358

AMA Style

Juraev DA, Shokri A, Marian D. Solution of the Ill-Posed Cauchy Problem for Systems of Elliptic Type of the First Order. Fractal and Fractional. 2022; 6(7):358. https://doi.org/10.3390/fractalfract6070358

Chicago/Turabian Style

Juraev, Davron Aslonqulovich, Ali Shokri, and Daniela Marian. 2022. "Solution of the Ill-Posed Cauchy Problem for Systems of Elliptic Type of the First Order" Fractal and Fractional 6, no. 7: 358. https://doi.org/10.3390/fractalfract6070358

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