Elmira ABDYLDAEVA, Gulbarchyn Taalaibek KYZY, Bermet NARKULOVA

Generalized solution of boundary value problem with an inhomogeneous boundary condition

In this problem, we study the solution to boundary value problem for a controlled oscillation process, described by Fredholm integro-differential equation with an inhomogeneous boundary condition. An algorithm is developed for constructing a generalized solution of boundary value problem. It is proved that a weak generalized solution is an element of Hilbert space. Approximate solutions of the boundary value problem are determined and their convergence is proved.

Keywords:

Boundary value problem, Boundary control conditıon Generalized solution, İntegral equation, Fourier series,

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[1] Vladimirov V.S.,” Matematicheskie zadachi odnoskorostnoi toerii perenosa chastis”, Trudy MİAN,Т.61,(1961),130-158.
[2] Volterra V., Teoriya funksionalov,integrelnyh i integro- differensiyalnyh uravneniy.Moskva, Nauka, 1982..
[3] Tyn Myint-U, Lokenath, Partial Differential Equations for Scientists and Engineers, Prentice Hall, 1987.
[4] Tihonov A.I. and Samarskiy А.А., Uravneniye matematicheskoy fiziki. Мoskva, Nauka,1972.
[5] Sharma J.N., Kehar Singh, Partial Differential Equations For Engineers and Scientists, Alpha Science İnternational Ltd. 2000, UK.
[6] Aramanovich İ.G. and Levin V.İ., Uravneniye matematicheskoy fiziki. İzdatelstvo Nauka, 1969.
[7] Denemeyer R. Introduction to: Partial Differential Equations and Boundary Value Problems, McGraw-Hill Book Company, New York, 1968.
[8] Snedon I.N., Elements of Partial Differential Equations, dover Publications, INC.,New York ,2006.
[9] Chaglıyan M., Chelebi O., Kysmi Diferensiyel Denklemler, Uludag Üniversitesi Guchlendirme Vakfı,Yayın No:196,VİPASH A.SH.,Yayın No:72,2002.
[10] Koca K., Kysmi Diferensiyel Denklemler, Gunduz Egitim ve Yayıncılık, Ankara, 2001.
[11] Anar E., Kısmi Diferensiyel Denklemler, Palme Yayıncılık,Ankara,2005.
[12] Kerimbekov A., Abdyldaeva E., “On the Solvability of a Nonlinear Tracking Problem Under Boundary Control for the Elastic Oscillations Described by Fredholm Integro-Differential Equations”, System Modeling and Optimization Dergisi. 27th IFIP TC 7 Conference, CSMO 2015. Sophia Antipolis, France, June 29–July 3, 2015. Revised Selected Papers. Sprınger. 2017. 312-322 р

ISSN: 1694-7398
Yayın Aralığı: Yılda 2 Sayı
Başlangıç: 2001
Yayıncı: KIRGIZİSTAN-TÜRKİYE MANAS ÜNİVERSİTESİ

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