Research Article
Year 2018,
Volume: 39 Issue: 3, 565 - 572, 30.09.2018
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.
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.
Year 2018,
Volume: 39 Issue: 3, 565 - 572, 30.09.2018
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.
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 | Natural Sciences |
| Authors | |
| Publication Date | September 30, 2018 |
| Submission Date | August 1, 2018 |
| Acceptance Date | September 11, 2018 |
| Published in Issue | Year 2018Volume: 39 Issue: 3 |