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Article information
2017 , Volume 22, ¹ 3, p.103-114
Fayazov K.S., Khazhiev I.O.
Ill-posed initial-boundary value problem for a system of parabolic equations with varying direction of time
Purpose. Proof of the uniqueness and conditional stability of the initial-boundary value problem for a system of parabolic type equations with varying direction of time, as well as constructing approximate solutions which are stable to variation of data. Methodology. The method of generalized spectral decomposition, the methods of logarithmic convexity and energy integrals and the method of regularization are used. Findings. Set of correctness is found. The uniqueness and conditional stability theorems are proved. Corresponding estimations of conditional stability are obtained, an approximate solution stable on the correctness set is constructed. Estimates of closeness between the exact and approximate solutions are obtained, formulas for the regularization parameter are derived. Originality/value. The conditional correctness of the initial-boundary value problem for a system of parabolic type equations with varying direction of time has been proved. A representation of the solution and approximate solutions are obtained. The numerical results show the possibility of a stable numerical solution of the required problem depending on the choice of the regularization parameter and the correctness set.
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Keywords: system of equations , boundary value problem, ill-posed problems, a priori estimate, theorem of the uniqueness, estimate of conditional stability, regularization, parameter of regularization
Author(s):
Fayazov Kudratillo Sadridinovich
Dr. , Professor
Position: Professor
Office: Turin Polytechnic University in Tashkent
Address: 100174, Uzbekistan, Tashkent, Kichik Khalka Yuli Str. 17
Phone Office: (99897)7370352
E-mail: kfayazov@yahoo.com
Khazhiev Ikrombek Ozodovich
Position: Senior Fellow
Office: National University of Uzbekistan
Address: 100174, Uzbekistan, Tashkent, 1 Universitetskaya str.
Phone Office: (99890)9931637
E-mail: h.ikrom@mail.ru
Bibliography link:
Fayazov K.S., Khazhiev I.O. Ill-posed initial-boundary value problem for a system of parabolic equations with varying direction of time // Computational technologies. 2017. V. 22. ¹ 3. P. 103-114
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