Research Article
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Denklemi için Bir Kuvvetli Kötü Konulmuş Problem

Year 2018, Volume: 39 Issue: 3, 565 - 572, 30.09.2018

Mustafa Yıldız

https://doi.org/10.17776/csj.450207
https://izlik.org/JA93SF43HJ

Abstract

Bu çalışmada eliptik denklem için Hadamard
anlamında kuvvetli kötü konulmuş olan bir ters problem ele alınmıştır. Bu
problemin çözümünün tekliği Carleman değerlendirmeleri yardımıyla
ispatlanmıştır.

Keywords

Eliptik denklem Ters problem Carleman değerlendirmesi

References

  • [1]. Amirov, A. Kh., Integral Geometry and Inverse Problems for Kinetic Equations. Utrecht, The Netherlands: VSP, 2001.
  • [2]. Gölgeleyen, F. and Yamamoto, M., An inverse problem for the Vlasov–Poisson system. Journal of Inverse and Ill-posed Problems, 23-4 (2015) 363-372.
  • [3]. Gölgeleyen, I., An integral geometry problem along geodesics and a computational approach. An. Univ.“Ovidius” Constanţa, Ser. Mat, 18-2 (2010) 91-112.
  • [4]. Lavrent’ev, M. M., Some Improperly Posed Problems of Mathematical Physics. New York: Springer-Verlag, 1967.
  • [5]. Lavrent’ev, M. M., Romanov, V. G. and Shishatskii, S. P., Ill-Posed Problems of Mathematical Physics and Analysis. Providence: American Mathematical Society, 1986.
  • [6]. Mikhailov, V.P., Partial Differential Equations. 2nd ed. Moscow: Mir Publishers, 1978.

A Strongly Ill-Posed Problem for the Equation

Year 2018, Volume: 39 Issue: 3, 565 - 572, 30.09.2018

Mustafa Yıldız

https://doi.org/10.17776/csj.450207
https://izlik.org/JA93SF43HJ

Abstract

In this work, we consider an inverse problem for an elliptic equation
which is strongly ill-posed in Hadamard sense. We prove the uniqueness of the
solution of the problem by using Carleman estimates.

Keywords

Elliptic equation Inverse problem Carleman estimate

References

  • [1]. Amirov, A. Kh., Integral Geometry and Inverse Problems for Kinetic Equations. Utrecht, The Netherlands: VSP, 2001.
  • [2]. Gölgeleyen, F. and Yamamoto, M., An inverse problem for the Vlasov–Poisson system. Journal of Inverse and Ill-posed Problems, 23-4 (2015) 363-372.
  • [3]. Gölgeleyen, I., An integral geometry problem along geodesics and a computational approach. An. Univ.“Ovidius” Constanţa, Ser. Mat, 18-2 (2010) 91-112.
  • [4]. Lavrent’ev, M. M., Some Improperly Posed Problems of Mathematical Physics. New York: Springer-Verlag, 1967.
  • [5]. Lavrent’ev, M. M., Romanov, V. G. and Shishatskii, S. P., Ill-Posed Problems of Mathematical Physics and Analysis. Providence: American Mathematical Society, 1986.
  • [6]. Mikhailov, V.P., Partial Differential Equations. 2nd ed. Moscow: Mir Publishers, 1978.
There are 6 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Mustafa Yıldız

Submission Date August 1, 2018
Acceptance Date September 11, 2018
Publication Date September 30, 2018
DOI https://doi.org/10.17776/csj.450207
IZ https://izlik.org/JA93SF43HJ
Published in Issue Year 2018 Volume: 39 Issue: 3

Cite

APA Yıldız, M. (2018). A Strongly Ill-Posed Problem for the Equation. Cumhuriyet Science Journal, 39(3), 565-572. https://doi.org/10.17776/csj.450207

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