The solution of an infinite system of ternary differential equations

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dc.citation.epage841
dc.citation.issue4
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage833
dc.contributor.affiliationУніверситет цифрової економіки та агротехнологій
dc.contributor.affiliationАндижанський державний університет
dc.contributor.affiliationНаціональний університет Узбекистану
dc.contributor.affiliationУніверситет Путра Малайзія
dc.contributor.affiliationUniversity of Digital Economics and Agrotechnologies
dc.contributor.affiliationAndijan State University
dc.contributor.affiliationNational University of Uzbekistan
dc.contributor.affiliationUniversiti Putra Malaysia
dc.contributor.authorІбрагімов, Г.
dc.contributor.authorКошаков, Х.
dc.contributor.authorТургунов, І.
dc.contributor.authorАліас, І. А.
dc.contributor.authorIbragimov, G.
dc.contributor.authorQo'shaqov, H.
dc.contributor.authorTurgunov, I.
dc.contributor.authorAlias, I. A.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-24T09:14:12Z
dc.date.created2022-02-28
dc.date.issued2022-02-28
dc.description.abstractСтаття присвячена нескінченній системі диференціальних рівнянь. Ця система складається з потрійних диференціальних рівнянь, що відповідають 3 × 3 жордановим блокам. Система розглядається в гільбертовому просторі l2. Доведено теорему про існування та єдиність розв’язку системи.
dc.description.abstractThe present paper is devoted to an infinite system of differential equations. This system consists of ternary differential equations corresponding to 3×3 Jordan blocks. The system is considered in the Hilbert space l2. A theorem about the existence and uniqueness of solution of the system is proved.
dc.format.extent833-841
dc.format.pages9
dc.identifier.citationThe solution of an infinite system of ternary differential equations / G. Ibragimov, H. Qo'shaqov, I. Turgunov, I. A. Alias // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 4. — P. 833–841.
dc.identifier.citationenThe solution of an infinite system of ternary differential equations / G. Ibragimov, H. Qo'shaqov, I. Turgunov, I. A. Alias // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 9. — No 4. — P. 833–841.
dc.identifier.doidoi.org/10.23939/mmc2022.04.833
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/64241
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 4 (9), 2022
dc.relation.ispartofMathematical Modeling and Computing, 4 (9), 2022
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dc.relation.references[2] Albeverio S., Alimov Sh. A. On a time-optimal control problem associated with the heat exchange process. Applied Mathematics and Optimization. 57 (1), 58–68 (2008).
dc.relation.references[3] Fursikov A. V. Optimal Control of Distributed Systems. Theory and Applications. Translations of Mathematical Monographs. Vol. 187. Amer. Math. Soc., Providence, Rhode Island (2000).
dc.relation.references[4] Chernous’ko F. L. Bounded controls in distributed-parameter systems. Journal of Applied Mathematics and Mechanics. 56 (5), 707–723 (1992).
dc.relation.references[5] Avdonin S. A., Ivanov S. A. Families of Exponentials: The Method of Moments in Controllability Problems for Distributed Parameter Systems. Cambridge, Cambridge University Press (1995).
dc.relation.references[6] Ibragimov G. A problem of optimal pursuit in systems with distributed parameters. Journal of Applied Mathematics and Mechanics. 66 (5), 719–724 (2002).
dc.relation.references[7] Tukhtasinov M. Some problems in the theory of differential pursuit games in systems with distributed parameters. Journal of Applied Mathematics and Mechanics. 59 (6), 935–940 (1995).
dc.relation.references[8] Tukhtasinov M., Mamatov M. Sh. On pursuit problems in controlled distributed parameters systems. Mathematical Notes. 84 (2), 256–262 (2008).
dc.relation.references[9] Ladyzhenskaya O. A. Kraevye zadachi matematicheskoy fiziki. Moscow (1973), (in Russian).
dc.relation.references[10] Satimov N. Yu., Tukhtasinov M. Game problems on a fixed interval in controlled first-order evolution equations. Mathematical Notes. 80 (3–4), 578–589 (2006).
dc.relation.references[11] Satimov N. Yu., Tukhtasinov M. On Some Game Problems for First-Order Controlled Evolution Equations. Differential Equations. 41 (8), 1169–1177 (2005).
dc.relation.references[12] Tukhtasinov M., Mamadaliyev N. On the Problems of Pursuit and Deviation from Meeting in the Class of the Distributed Control Systems. ROMAI Journal. 7 (2), 161–168 (2011).
dc.relation.references[13] Azamov A. A., Ruziboev M. B. The time-optimal problem for evolutionary partial differential equations. Journal of Applied Mathematics and Mechanics. 77 (2), 220–224 (2013).
dc.relation.references[14] Satimov N. Yu., Tukhtasinov M. On game problems for second-order evolution equations. russian mathematics. Russian Mathematics. 51 (1), 49–57 (2007).
dc.relation.references[15] Ibragimov G., Allahabi F., Kuchkarov A. Sh. A pursuit problem in an infinite system of second-order differential equations. Ukrainian Mathematical Journal. 65 (8), 1203–1216 (2014).
dc.relation.references[16] Ibragimov G., Risman M. H. Pursuit and Evasion Differential Game in Hilbert space. International Game Theory Review. 12 (3), 239–251 (2010).
dc.relation.references[17] Ibragimov G. Optimal pursuit time for a differential game in the Hilbert space l2. Science Asia. 39S, 25–30 (2013).
dc.relation.references[18] Ibragimov G., Norshakila A. R., Kuchkarov A., Fudziah I. Multi Pursuer Differential Game of Optimal Approach with Integral Constraints on Controls of Players. Taiwanese Journal of Mathematics. 19 (3), 963–976 (2015).
dc.relation.references[19] Alias I. A., Ibragimov G., Rakhmanov A. Evasion Differential Game of Infinitely Many Evaders from Infinitely Many Pursuers in Hilbert Space. Dynamic Games and Applications. 7, 347–359 (2016).
dc.relation.references[20] Ibragimov G. On possibility of evasion in a differential game, described by countable number differential equations. Uzbek Mathematical Journal. 1, 42–47 (2004), (in Russian).
dc.relation.references[21] Ibragimov G., Azamov A., Risman M. H. Existence and Uniqueness of the Solution for an Infinite System of Differential Equations. Journal KALAM, International Journal of Mathematics and Statistics. 1 (2), 9–14 (2008).
dc.relation.referencesen[1] Butkovskiy A. G. Theory of Optimal Control of Distributed Parameter Systems. New York, Elsevier (1969).
dc.relation.referencesen[2] Albeverio S., Alimov Sh. A. On a time-optimal control problem associated with the heat exchange process. Applied Mathematics and Optimization. 57 (1), 58–68 (2008).
dc.relation.referencesen[3] Fursikov A. V. Optimal Control of Distributed Systems. Theory and Applications. Translations of Mathematical Monographs. Vol. 187. Amer. Math. Soc., Providence, Rhode Island (2000).
dc.relation.referencesen[4] Chernous’ko F. L. Bounded controls in distributed-parameter systems. Journal of Applied Mathematics and Mechanics. 56 (5), 707–723 (1992).
dc.relation.referencesen[5] Avdonin S. A., Ivanov S. A. Families of Exponentials: The Method of Moments in Controllability Problems for Distributed Parameter Systems. Cambridge, Cambridge University Press (1995).
dc.relation.referencesen[6] Ibragimov G. A problem of optimal pursuit in systems with distributed parameters. Journal of Applied Mathematics and Mechanics. 66 (5), 719–724 (2002).
dc.relation.referencesen[7] Tukhtasinov M. Some problems in the theory of differential pursuit games in systems with distributed parameters. Journal of Applied Mathematics and Mechanics. 59 (6), 935–940 (1995).
dc.relation.referencesen[8] Tukhtasinov M., Mamatov M. Sh. On pursuit problems in controlled distributed parameters systems. Mathematical Notes. 84 (2), 256–262 (2008).
dc.relation.referencesen[9] Ladyzhenskaya O. A. Kraevye zadachi matematicheskoy fiziki. Moscow (1973), (in Russian).
dc.relation.referencesen[10] Satimov N. Yu., Tukhtasinov M. Game problems on a fixed interval in controlled first-order evolution equations. Mathematical Notes. 80 (3–4), 578–589 (2006).
dc.relation.referencesen[11] Satimov N. Yu., Tukhtasinov M. On Some Game Problems for First-Order Controlled Evolution Equations. Differential Equations. 41 (8), 1169–1177 (2005).
dc.relation.referencesen[12] Tukhtasinov M., Mamadaliyev N. On the Problems of Pursuit and Deviation from Meeting in the Class of the Distributed Control Systems. ROMAI Journal. 7 (2), 161–168 (2011).
dc.relation.referencesen[13] Azamov A. A., Ruziboev M. B. The time-optimal problem for evolutionary partial differential equations. Journal of Applied Mathematics and Mechanics. 77 (2), 220–224 (2013).
dc.relation.referencesen[14] Satimov N. Yu., Tukhtasinov M. On game problems for second-order evolution equations. russian mathematics. Russian Mathematics. 51 (1), 49–57 (2007).
dc.relation.referencesen[15] Ibragimov G., Allahabi F., Kuchkarov A. Sh. A pursuit problem in an infinite system of second-order differential equations. Ukrainian Mathematical Journal. 65 (8), 1203–1216 (2014).
dc.relation.referencesen[16] Ibragimov G., Risman M. H. Pursuit and Evasion Differential Game in Hilbert space. International Game Theory Review. 12 (3), 239–251 (2010).
dc.relation.referencesen[17] Ibragimov G. Optimal pursuit time for a differential game in the Hilbert space l2. Science Asia. 39S, 25–30 (2013).
dc.relation.referencesen[18] Ibragimov G., Norshakila A. R., Kuchkarov A., Fudziah I. Multi Pursuer Differential Game of Optimal Approach with Integral Constraints on Controls of Players. Taiwanese Journal of Mathematics. 19 (3), 963–976 (2015).
dc.relation.referencesen[19] Alias I. A., Ibragimov G., Rakhmanov A. Evasion Differential Game of Infinitely Many Evaders from Infinitely Many Pursuers in Hilbert Space. Dynamic Games and Applications. 7, 347–359 (2016).
dc.relation.referencesen[20] Ibragimov G. On possibility of evasion in a differential game, described by countable number differential equations. Uzbek Mathematical Journal. 1, 42–47 (2004), (in Russian).
dc.relation.referencesen[21] Ibragimov G., Azamov A., Risman M. H. Existence and Uniqueness of the Solution for an Infinite System of Differential Equations. Journal KALAM, International Journal of Mathematics and Statistics. 1 (2), 9–14 (2008).
dc.rights.holder© Національний університет “Львівська політехніка”, 2022
dc.subjectдиференціальне рівняння
dc.subjectнескінченна система
dc.subjectіснування та єдиність розв’язку
dc.subjectгільбертовий простір
dc.subjectdifferential equation
dc.subjectinfinite system
dc.subjectexistence and uniqueness of solution
dc.subjectHilbert space
dc.titleThe solution of an infinite system of ternary differential equations
dc.title.alternativeРозв’язок нескінченної системи потрійних диференціальних рівнянь
dc.typeArticle

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Mathematical Modeling And Computing. – 2022. – Vol. 9, No. 4