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Russian Mathematics

, Volume 63, Issue 6, pp 8–18 | Cite as

A Linear Inverse Problem for a Multidimensional Mixed-Type Second-Order Equation of the First-Kind

  • S. Z. DzhamalovEmail author
  • R. R. AshurovEmail author
Article

Abstract

In this paper, we study the well-posedness of a linear inverse problem for a mixed-type second-order multidimensional equation of the first kind. We prove the unique solvability of this problem in a certain function class with the help of “ε-regularization”, a priori estimates, and successive approximation methods.

Key words

multidimensional mixed-type second-order equation of the first kind linear inverse problem correctness of solution “ε-regularization ”methods a priori estimate successive approximation 

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Notes

Acknowledgments

The authors are grateful to the academician of the Academy of Sciences of Republic of Uzbekistan Shavkat Arifzhanovich Alimov for the discussion of results obtained in this paper and for valuable advices, and to the reviewer for useful remarks.

Funding

This work was performed in accordance with the research plan OT-FA-88 and supported by the grant MRU-OT-1/2017.

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Copyright information

© Allerton Press, Inc. 2019

Authors and Affiliations

  1. 1.Institute of MathematicsUzbekistan Academy of SciencesAkademgorodok, TashkentRepublic of Uzbekistan
  2. 2.Gubkin Russian State University of Oil and Gas of TashkentTashkentRepublic of Uzbekistan
  3. 3.National University of Uzbekistan named aftar M. UlugbekTashkentRepublic of Uzbekistan

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