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İkinci Mertebeden Periyodik ve İntegral Koşullu Eliptik Denklemler İçin Ters Sınır-Değer Problemlerin Çözümü

Year 2019, Volume: 40 Issue: 2, 355 - 368, 30.06.2019
https://doi.org/10.17776/csj.489939

Abstract

Sunulan
çalışmada dikdörtgensel bölgede periyodik ve integral tipli koşullarla verilen
ikinci mertebeden eliptik tip diferansiyel denklemler için bazı ters
problemlerin çözümü ele alınmıştır. Matematiksel fiziğin denklemleri için ters
problemler olarak verilen denklemlerin çözümü ile ilgili bilinen ek bilgiler
yardımıyla onun katsayıların veya sağ taraftaki fonksiyonların, veya katsayıların
ve sağ taraftaki bilinmeyen fonksiyonların birlikte belirlenmesi problemleri
düşünülmektedir. Ters problemler bilimin birçok dallarında ortaya çıkmakta
olup, özellikle fiziksel ve kimyasal süreçlerin takibi sırasında bazı
büyüklüklerin belirlenmesinde önem taşımaktadır. Genelde fiziksel
 
ve kimyasal süreçler diferansiyel denklemlerle ifade
edildiğinden ve bu diferansiyel denklemlerin katsayıları da süreçleri ifade
eden fiziksel ve kimyasal büyüklüklere bağlı olduğundan, süreçlerin akışının
belirlenmesi için bu süreci ifade eden diferansiyel denklemin katsayılarının
belirlenmesi önemlidir. Dolayısıyla, ters problemlerin konumu ve çözümü
bilimsel açıdan çok önem taşımaktadır
.

References

  • [1] Tikhonov A.N., On stability of inverse problems, Dokl. AN SSSR, 39(1943), no. 5, 195–198 (in Russian).
  • [2] Lavrent’ev M.M., On an inverse problem for a wave equation, Dokl. AN SSSR, 157(1964), no. 3, 520–521 (in Russian).
  • [3] Lavrent’ev M.M., Romanov V.G., Shishatsky S.T. Ill-posed problems of mathematical physics and analysis, M., Nauka, 1980 (in Russian).
  • [4] Ivanov V.K., Vasin V.V., Tanana V.P., Theory of linear ill-posed problems and its applications, M., Nauka, 1978 (in Russian).
  • [5] Denisov A.M., Introduction to theory of inverse problems, M., MGU, 1994 (in Russian).
  • [6] Mehraliyev Ya.T., On solvability of an inverse boundary value problem for a second order elliptic equation, Vest. Tverskogo Gos. Univ., Ser. prikladnaya matematika, (2011), no. 23, 25–38 (in Russian).
  • [7] Budak B.M., Samarskii A.A.,.Tikhonov A.N, A Collection of Problems in Mathematical Physics, M., Nauka, 1972 (in Russian).

On Solvability of An Inverse Boundary Value Problem For The Elliptic Equation Of Second Order With Periodic And Integral Condition

Year 2019, Volume: 40 Issue: 2, 355 - 368, 30.06.2019
https://doi.org/10.17776/csj.489939

Abstract



An inverse boundary value problem for a
second-order elliptic equation with periodic and integral condition is
investigated. The definition of a classical solution of the problem is
introduced. The goal of this paper is to determine the unknown coefficient and
to solve the problem of interest. The problem is considered in a rectangular
domain. To investigate the solvability of the inverse problem, we perform a
conversion from the original problem to some auxiliary inverse problem with
trivial boundary conditions. By the contraction mapping principle we prove the
existence and uniqueness of solutions of the auxiliary problem. Then we make a
conversion to the stated problem again and, as a result, we obtain the
solvability of the inverse problem.



References

  • [1] Tikhonov A.N., On stability of inverse problems, Dokl. AN SSSR, 39(1943), no. 5, 195–198 (in Russian).
  • [2] Lavrent’ev M.M., On an inverse problem for a wave equation, Dokl. AN SSSR, 157(1964), no. 3, 520–521 (in Russian).
  • [3] Lavrent’ev M.M., Romanov V.G., Shishatsky S.T. Ill-posed problems of mathematical physics and analysis, M., Nauka, 1980 (in Russian).
  • [4] Ivanov V.K., Vasin V.V., Tanana V.P., Theory of linear ill-posed problems and its applications, M., Nauka, 1978 (in Russian).
  • [5] Denisov A.M., Introduction to theory of inverse problems, M., MGU, 1994 (in Russian).
  • [6] Mehraliyev Ya.T., On solvability of an inverse boundary value problem for a second order elliptic equation, Vest. Tverskogo Gos. Univ., Ser. prikladnaya matematika, (2011), no. 23, 25–38 (in Russian).
  • [7] Budak B.M., Samarskii A.A.,.Tikhonov A.N, A Collection of Problems in Mathematical Physics, M., Nauka, 1972 (in Russian).
There are 7 citations in total.

Details

Primary Language English
Journal Section Natural Sciences
Authors

Rauf Amırov 0000-0001-6754-2283

Y.t. Mehralıyev 0000-0002-2054-3219

N.a. Heydarzade

Publication Date June 30, 2019
Submission Date November 29, 2018
Acceptance Date March 19, 2019
Published in Issue Year 2019Volume: 40 Issue: 2

Cite

APA Amırov, R., Mehralıyev, Y., & Heydarzade, N. (2019). On Solvability of An Inverse Boundary Value Problem For The Elliptic Equation Of Second Order With Periodic And Integral Condition. Cumhuriyet Science Journal, 40(2), 355-368. https://doi.org/10.17776/csj.489939