On the solvability of the Cauchy problem for the Biharmonic equation
##submission.downloads##
Ushbu tadqiqot Bigarmonik tenglama uchun Koshi masalasining yechiluvchanligini o‘rganishga
bag‘ishlangan. Avvalo, Koshi masalasining integral shaklda ifodalangan yechimini olamiz. So‘ngra
berilgan masalaning yechimining mavjudligi va yagonaligi isbotlanadi.
1. A. N. Tikhonov, A. A. Samarsky, Equations of Mathematical Physics, Nauka, Moscow (Russian), 1966.
2. A. Gavrikov, G. Kostin, Heat Transfer Processes in a Cylindrical Body Surrounded by Air, Proc. of 59th
MIPT Scientific Conference, Moscow, Russia, 2016 (Russian).
3. J. Hadamard, Lectures on Cauchy’s problem in linear partial differential equations. New Haven: Yale
University Press; London: Humphrey Milford; Oxford: University Press. VIII u. 316 S., 1923.
4. S. I. Kabanikhin, Inverse and Ill-posed Problems: Theory and Applications, Walter de Gruyter GmbH &
Co. KG, Berlin/Boston, Inverse Ill-posed Probl. Ser. 55, 2012.
5. T. Sh. Kal’menov and U. A. Iskakova, Criterion for the Strong Solvability of the Mixed Cauchy Problem
for the Laplace Equation, Differential Equations, 2009, Vol. 45, No. 10, pp. 1460-1466.
6. M. M. Lavrentyev, On the Cauchy problem for Laplace equation. Izv. Akad. Nauk SSSR. Ser. Mat.,
20:819-842, 1956.
7. T. Sh. Kal’menov and U. A. Iskakova, On an Ill-posed Problem for a Biharmonic Equation, University of
Nis, Faculty of Sciences and Mathematics, 2017, Vol. 31, No. 4, pp. 1051-1056.
8. A. N. Tikhonov, Non-linear equations of first kind, Doklady akademii nauk SSSR, 161:5 (1965), 1023-1026.
(in Russian)
9. S. Mizohata, The Theory of Partial Differential Equations. London: Cambridge University Press. XI,490
p. (1973).
10. M. A. Naimark, Linear Differential Operators (Russian), 2nd Edition, Nauka, Moscow, 1969, p. 1-528.
11. W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, 1964.
12. A. N. Tikhonov, A. V. Goncharsky, V. V. Stepanov, A. G. Yagola, Numerical Methods for the Solution
of Ill-Posed Problems, Kluwer Academic Publishers, 1995.
13. M. A. Atakhodzhaev, Ill-posed internal boundary value problems for the biharmonic equation, Inverse
and Ill-Posed Problems Series 35, De Gruyter, 2002.
14. Sh. A. Alimov, A. K. Qudaybergenov, Determination of temperature at the outer boundary of a body,
Journal of Mathematical Sciences, Vol. 274, No. 2, August, 2023, pp.159-171.
15. Sh. A. Alimov, A. K. Qudaybergenov, On the determining of the stationar temperature in the unbounded
stripe, Differential equations, Vol. 0, No. 8, 2024, pp.1049-1062.
16. Sh. A. Alimov, A. K. Qudaybergenov, On the solvability of the Cauchy Problem for Laplace equation,
Uzbek Mathematical Journal, 2022, Volume 66, Issue 3, pp.5-14 DOI: 10.29229/uzmj.2022-4-1.
Mulkiiyat (c) 2025 «O‘zMU XABARLARI»

Ushbu ish quyidagi litsenziya asosida ruxsatlangan Kreativ Commons Attribution-NonCommercial-ShareAlike 4.0 International litsenziyasi asosida bu ish ruxsatlangan..


.jpg)

.png)






