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NUMERICAL SOLUTION OF AN INVERSE PROBLEM FOR THE LIOUVILLE EQUATION

Yıl 2019, Cilt: 9 Sayı: 4, 909 - 920, 01.12.2019

Öz

We consider an inverse problem for the Liouville Equation. We present the solvability conditions and obtain numerical solution of the problem based on the nite di erence approximation.

Kaynakça

  • Amirov, A. Kh., (2001), Integral Geometry and Inverse Problems for Kinetic Equations, VSP, Utrecht, The Netherlands.
  • Anikonov, Yu. E. and Amirov, A. Kh., (1983), A uniqueness theorem for the solution of an inverse problem for the kinetic equation, Dokl. Akad. Nauk SSSR., 272 (6), pp. 1292-1293.
  • Anikonov, Yu. E., (2001), Inverse Problems for Kinetic and other Evolution Equations, VSP, Utrecht, The Netherlands.
  • Zhenglu, J., (2002), On the Liouville equation, Transport theory and statistical physics, 31 (3), pp. 267-272.
  • Prilepko, A. I., Orlovsky, D. G. and Vasin, I. A., (2000), Methods for Solving Inverse Problems in Mathematical Physics, Marcel Dekker, Inc., New York.
  • G¨olgeleyen, I., (2013), An inverse problem for a generalized transport equation in polar coordinates and numerical applications, Inverse problems, 29 (9), 095006.
  • Amirov, A., Ustao˘glu, Z. and Heydarov, B., (2011), Solvability of a two dimensional coefficient inverse problem for transport equation and a numerical method, Transport theory and statistical physics, 40 (1), pp. 1-22.
  • Amirov, A., G¨olgeleyen, F. and Rahmanova, A., (2009), An inverse problem for the general kinetic equation and a numerical method, CMES, 43 (2), pp. 131-147.
  • Liboff, R. L., (2003), Kinetic Theory: Classical, Quantum, and Relativistic Descriptions, 3rd ed. Springer-Verlag, New York.
Yıl 2019, Cilt: 9 Sayı: 4, 909 - 920, 01.12.2019

Öz

Kaynakça

  • Amirov, A. Kh., (2001), Integral Geometry and Inverse Problems for Kinetic Equations, VSP, Utrecht, The Netherlands.
  • Anikonov, Yu. E. and Amirov, A. Kh., (1983), A uniqueness theorem for the solution of an inverse problem for the kinetic equation, Dokl. Akad. Nauk SSSR., 272 (6), pp. 1292-1293.
  • Anikonov, Yu. E., (2001), Inverse Problems for Kinetic and other Evolution Equations, VSP, Utrecht, The Netherlands.
  • Zhenglu, J., (2002), On the Liouville equation, Transport theory and statistical physics, 31 (3), pp. 267-272.
  • Prilepko, A. I., Orlovsky, D. G. and Vasin, I. A., (2000), Methods for Solving Inverse Problems in Mathematical Physics, Marcel Dekker, Inc., New York.
  • G¨olgeleyen, I., (2013), An inverse problem for a generalized transport equation in polar coordinates and numerical applications, Inverse problems, 29 (9), 095006.
  • Amirov, A., Ustao˘glu, Z. and Heydarov, B., (2011), Solvability of a two dimensional coefficient inverse problem for transport equation and a numerical method, Transport theory and statistical physics, 40 (1), pp. 1-22.
  • Amirov, A., G¨olgeleyen, F. and Rahmanova, A., (2009), An inverse problem for the general kinetic equation and a numerical method, CMES, 43 (2), pp. 131-147.
  • Liboff, R. L., (2003), Kinetic Theory: Classical, Quantum, and Relativistic Descriptions, 3rd ed. Springer-Verlag, New York.
Toplam 9 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

F. Gölgeleyen Bu kişi benim

M. Hasdemir Bu kişi benim

Yayımlanma Tarihi 1 Aralık 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 9 Sayı: 4

Kaynak Göster