Bulletin KRASEC. Phys. & Math. Sci. 2016. V. 13. no. 2. pp. 10-15. ISSN 2313-0156

Back to contents

DOI: 10.18454/2313-0156-2016-13-2-10-15

MSC 34L99

LINEAR INVERSE PROBLEM FOR TRIKOMI EQUATION IN THREE-DIMENSIONAL SPACE

S. Z. Djamalov

Institute of Мathematics, National University of Uzbekistan, Tashkent, 100125, Academgorodok, Do’rmon yo’li, 29 str.
E-mail: siroj63@mail.ru

In the present work the problems of correctness of a linear inverse problem for Trikomi equation in three-dimensional space are considered. For this problem, the theorems on existence and uniqueness of the solution in a certain class are proved by «e-regularization Galerkin’s methods and by the method of successive approximations.

Key words: Trikomi equations, linear inverse problem, correctness of solution, Galerkin’s method, « e-regularization» method, method of successive approximations.

 

References

  1. Anikonov Yu. E. Nekotorye metody issledovaniya mnogomernykh obratnykh zadach dlya differentsial’nykh uravneniy [Some methods of investigation of inverse problems for differential equations]. Novosibirsk. Nauka. 1978. 120 p.
    2. Bubnov B. A. K voprosu o razreshimosti mnogomernykh obratnykh zadach dlya parabolicheskikh i giperbolicheskikh uravneniy [The question on the solvability of multidimensional problems for parabolic and hyperbolic equations]. Novosibirsk. 1987. Preprints №713, №714, VTs.SO AN SSSR.
    3. Dzhamalov S. Z. O korrektnosti nekotorykh nelokal’nykh kraevykh zadach dlya uravneniya smeshannogo tipa pervogo roda [Correctness of some nonlocal boundary value problems for mixed equations of the first kind]. Kraevye zadachi dlya neklassicheskikh uravneniy matematicheskoy fiziki [Boundary value problems for non-classical equations of mathematical physics]. Novosibirsk. 1989. pp. 112–114.
    4. Dzhamalov S. Z. Ob odnoy lineynoy obratnoy zadache dlya uravneniya smeshannogo tipa vtorogo roda vtorogo poryadka v trekhmernom prostranstve [A linear reverse problem for mixed equation of the second kind in a three-dimensional space]. Uzbekskiy matematicheskiy zhurnal – The Uzbek Mathematical Journal. 2014. no. 4. pp. 29–35.
    5. Kozhanov A. I. Nelineynye nagruzhennye uravneniya i obratnye zadachi [Nonlinear loaded equations and inverse problems]. Zhurnal vychislitel’noy matematiki i matematicheskoy fiziki – Computational Mathematics and Mathematical Physics. 2004. vol. 44. no. 4. pp. 694–716.
    6. Sabitov K. B, Safin E. M. Obratnaya zadacha dlya uravneniya parabolo-giperbolicheskogo tipa v pryamougol’noy oblasti [Reverse problem for parabolic-hyperbolic equation in a rectangular domain]. Doklady RAN – Reports of the Russian Academy of Sciences. 2009. vol. 429. no. 4. pp. 451–454.
    7. Sabitov K. B., Martem’yanova N.V. Nonlocal reverse problem for mixed equation. Izvestiya vysshikh uchebnykh zavedeniy. Matematika – Russian Mathematics. 2011. no. 2. pp. 71–85.
    8. Lavrent’ev M. M, Romanov V. G, Vasil’ev V. G. Mnogomernye obratnye zadachi dlya differentsial’nykh uravneniy [Multidimensional reverse problems for differential equations]. Novosibirsk. Nauka. 1969. 67 p.
    9. Ladyzhenskaya O. A. Kraevye zadachi matematicheskoy fiziki [Boundary value problems of mathematical physics]. Moscow. Nauka. 1973. 407 p.
    10. Trenogin V. A. Funktsional’nyy analiz [Functional analysis]. Moscow. Nauka. 494 p.

For citation: Djamalov S. Z. Linear inverse problem for Trikomi equation in three-dimensional space. Bulletin KRASEC. Physical and Mathematical Sciences 2016, vol. 13, no 2, 10-15. DOI: 10.18454/2313-0156-2016-13-2-10-15

Original article submitted: 12.05.2016

Djam

Djamalov Sirojiddin Zuhriddinovich – Ph.D.(Phys & Math), Senior Researcher of department Differential equations, Institute of mathematics, National university of Uzbekistan, Tashkent, Republic of Uzbekistan.

Download article Djamalov S.Z.