ON THE ISSUE OF SOLUBILITY OF ONE BOUNDARY-VALUE PROBLEM FOR A PSEUDOHYPERBOLIC QUARTIC WITH AN ADDITIONAL INTEGRAL CONDITION 

Megraliev Yashar Topush ogly , Candidate of physical and mathematical sciences, associate professor, sub-department of differential and integral equations, Baku State University (Azerbaijan, Baku, 23 Academica Zakhid Khalilova str.), yashar_aze @ mail.ru 

517.95 

The article investigates an inverse problem for a pseudohyperbolic quartic with periodical boundary conditions. At first the initial problem is reduced to an equivalent problem, for which the author proves the theorem of existence and uniqueness. Then on the basis of these facts the researcher proves the existence and uniqueness of the classical solution of the initial problem. 

inverse boundary problem, pseudohyperbolic quartic, Fourier method, classic solution. 

1. Samarskiy, A. A. O nekotorykh problemakh teorii differentsial'nykh uravneniy / A. A. Samarskiy // Differentsial'nyye uravneniya. – 1980. – T. 16, № 11. – S. 1925– 1935.
2. Cannon, J. R. The solution of the heat equation subject to the specification of energy / J. R. Cannon // Quart. Appl. Math. – 1963. – V. 5, № 21. – P. 155–160.
3. Ionkin, N. I. Resheniye odnoy krayevoy zadachi teorii teploprovodnosti s neklassicheskim krayevym usloviyem / N. I. Ionkin // Differentsial'nyye uravneniya. – 1977. – T. 13, № 2. – S. 294–304.
4. Nakhushev, A. M. Ob odnom priblizhennom metode resheniya krayevykh zadach dlya differentsial'nykh uravneniy i yego priblizheniya k dinamike pochvennoy vlagi i gruntovykh vod / A. M. Nakhushev // Differentsial'nyye uravneniya. – 1982. – T. 18, № 1. – S. 72–81.
5. Kapustin, N. YU. O spektral'nykh zadachakh so spektral'nym parametrom v granichnom uslovii / N.YU.Kapustin, Ye. I. Moiseyev // Differentsial'nyye uravneniya. – 1997. – T. 33, № 1. – S. 115–119.
6. Kozhanov, A. I. O razreshimosti krayevykh zadach s nelokal'nym granichnym usloviyem integral'nogo vida dlya mnogomernykh giperbolicheskikh uravneniy / A. I. Kozhanov, L. S. Pul'kina // Differentsial'nyye uravneniya. – 2006. – T. 42, № 9. – S. 1166–1179.
7. Gordeziani, D. G. Resheniya nelokal'nykh zadach dlya odnomernykh kolebaniy sredy / D. G. Gordeziani, G.A.Avalishvili // Matematicheskoye modelirovaniye. – 2000. – T. 12, № 1. – S. 94–103.
8. Prilepko, A. I. O nekotorykh obratnykh zadachakh dlya parabolicheskikh uravneniy s final'nym i integral'nym nablyudeniyem / A. I. Prilepko, A. B. Kostin // Matematicheskiy sbornik. – 1992. – T. 183, № 4. – S. 49–68.
9. Prilepko, A. I. Svoystva resheniy parabolicheskogo uravneniya i yedinstven-nost' resheniya obratnoy zadachi ob istochnike s integral'nym pereopredeleniyem / A. I. Prilepko, D. S. Tkachenko // Zhurnal vychislitel'noy matematiki i matemati cheskoy fiziki. – 2003. – T. 43, № 4. – S. 562–570.
10. Kamynin, V. L. Ob obratnoy zadache opredeleniya pravoy chasti v parabolicheskom uravnenii s usloviyem integral'nogo pereopredeleniya / V. L. Kamynin // Matematicheskiye zametki. – 2005. – T. 77, № 4. – S. 522–534.
11. Gabasov, S. A. Ob uravnenii d²/dt²[Uxx - U]+ Uxx=0 i nekotorykh svyazannykh s nim zadachakh / S.A.Gabasov, B. B. Orazov // Zhurnal vychislitel'noy matematiki i matematicheskoy fiziki. – 1986. – T. 26, № 1. – S. 92–102.
12. Khudaverdiyev, K. I. Issledovaniye odnomernoy smeshannoy zadachi dlya odnogo klassa psevdogiperbolicheskikh uravneniy tret'yego poryadka s nelineynoy operatornoy pravoy chast'yu / K.I.Khudaverdiyev, A. A. Veliyev. – Baku : Chashyogly, 2010. – 168 s.