Durağan Olmayan Bir Kinetik Denklem İçin Bazı Düz ve Ters Problemler
Abstract
Bu çalışmada saçılım terimi içeren durağan olmayan bir kinetik denklem için bazı düz ve ters problemler ele alınmıştır. Bu problemlerin aralarındaki ilişki tartışılmış ve çözümlerinin tekliği araştırılmıştır.
Keywords
Kinetik denklem, Düz problem, Ters kaynak problemi, Çözümün tekliği
References
- Yu. E. Anikonov, “Inverse Problems for Kinetic and other Evolution Equations,” De Gruyter, 2001.
- A. K. Amirov, “Integral Geometry and Inverse Problems for Kinetic Equations,” VSP, Utrecht The Netherlands, 2001.
- A. Kh. Amirov, “Uniqueness of the solution of an inverse problem for kinetic equation,” Sibirsk. Mat. Zh., vol. 28, no. 5, pp. 3-5, 1987.
- F. Gölgeleyen, A. Amirov, “On the approximate solution of a coefficient inverse problem for the kinetic equation,” Mathematical Communications, vol. 16, no. 1, pp. 283-298, 2011.
- M. M Lavrentiev, V.G. Romanov, and S. P. Shishatskii, “Ill-Posed Problems of Mathematical Physics and Analysis,” American Mathematical Society, Providence, 1986. V. G. Romanov, “Integral Geometry and Inverse Problems for Hyperbolic Equations,” Springer-Verlag, 1974.
- J. Radon, “Über die Bestimmung von Funktionen durch ihre Integral-werte längs gewisser Mannigfaltigkeiten,” Berichte Sächsische Akademie der Wissenschaften, Leipzig, Math Nat kl. vol. 69, pp. 262–277, 1917.
- J. F. John, “Bestimmung einer Funktion aus ihren Integralen über gewisse Mannigfaltigkeiten,” Mathematische Annalen, vol. 109, no. 1, pp. 488-520, 1934.
- M. V. Klibanov, and A. A. Timonov, “Carleman Estimates for Coefficient Inverse Problems and Numerical Applications,” De Gruyter, 2012.
- M. Bellassoued, and M. Yamamoto, “Carleman Estimates and Applications to Inverse Problems for Hyperbolic Systems,” Tokyo, Springer Japan, 2017.
- V. Isakov, “Inverse Problems for Partial Differential Equations,” New York, Springer, vol. 127, 2016.