Функция Грина задачи Дирихле дифференциального оператора на графе - звезде при m
DOI:
https://doi.org/10.26577/JMMCS-2019-1-613Ключевые слова:
ориентированный граф, условия Кирхгофа, колебания упругих сетей, задача Дирихле, разложение по собственным функциямАннотация
В данной работе исследуется система дифференциальных уравнений второго порядка, являющейся моделью колебательных систем со стержневой конструкцией.Задачи для дифференциальных операторов на графах в ностоящее время активно изучаются математиками и имеют приложения в квантовой механике, органической химии, нанотехнологиях, теории волноводов и других областях естествознания. В данной статье выведена функция Грина задачи Дирихле для дифференциального оператора на звездообразном графе. Нами использованы стандартные условия склейки во внутренних вершинах и краевые условия Дирихле в граничных вершинах.
Библиографические ссылки
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[15] Pokornyi U.V., Priadiev V.L. Nekotorye problemy kachestvennoi teorii Shturma-Liuvillya na prostranstvennyh setyah [Some problems of the qualitative theory of Sturm-Liouville on spatial networks], Uspehi mat. nauk.2004. - V. 59, - P. 115-150.
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[19] P. Kurasov, M. Garjiani, Quantum graphs: PT-symmetry and reflection symmetry of the spectrum.// Journal of Mathematical Physics. 2017. - V.58.
[20] M. Astudillo, P. Kurasov, M. Usman, RT -symmetric laplace operators on star graphs: Real spectrum and selfadjointness. // Adv. Math. Phys. 2015.
[2] Pokornyi U.V. O spectre nekotoryh zadach na graphah [About the spectrum of some problems on the graph], Uspehi mat.nauk. 1987. - V. 42, P. 128-129.
[3] Penkin O.M. O krayevoi zadache na graphe [About boundary value problems on a graph], Differenciyalnye uravneniya 1988. - V. 24, - P. 701-703.
[4] Von Below J. Classical solvability of linear parabolic equations on networks, Differential Equation. 1988. - V.72, P. 316-337.
[5] Von Below J. Sturm-Liouville eigenvalue problems on networks, Math. Metli. Appl. Sc. 1988. - V.10, P.383-395.
[6] Lumer G. Connecting of local operators and evolution equations on network, Lect. Notes Math. 1980.- V.787 - P. 219-234.
[7] Nicaise S. Some results on spectral theory over networks, applied to nerve impuls transmission, Lect.Notes Math. 1985. - no 1771- P. 532-541.
[8] Pokornyi U.B. Differenciyalnye uravneniya na geometricheskih graphah [Differenciail equations on geometric graphs]. M.: Phizmatlit. 2004. - P. 272-274.
[9] Kanguzhin B.E. Funkciya Grina zadachi Dirihle dlya differencialnogo operatora na grafe-zvezde[Green’s function of Dirichlet problem for differential operators on a star-shaped graphs], Vestnik KazNU 2018. - P. 67-90.
[10] Bondarenko N.P. Partial inverse problems for the Sturm-Liouville operator on star-shaped graph with mixed boundary conditions, J. Inverse Ill - Posed Probl. 2018.- P.1-12
[11] Afanasev N.A., Bulot L.P. Electrotehnika i electronika[Electrotechnik and electronik], SPbGUN and P.T. 2010. P.181-183.
[12] Zavgorodnii M.G. Sopryazhennye i samosopryajennye krayvye zadachi na geometricheskom graphe [Conjugate and selfadjoint
boundary value problems on a geometric graph], Differencial equations. 2014. - V. 50, no 4- P. 446-456.
[13] Kurasov P., Stenberg F. On the inverse scattering problem on branching graphs, J. Phys. A. Math. Gen, 2002. - V. 20. - P. 647-672.
[14] Pokornyi U.V., Priadiev V.L., Al-Obeid A. Ob oscilyacionnyh svoistvah spectra kraevoi zadachi na graphe, Matem.zametki, 1996 - V.60. - P. 468-469.
[15] Pokornyi U.V., Priadiev V.L. Nekotorye problemy kachestvennoi teorii Shturma-Liuvillya na prostranstvennyh setyah [Some problems of the qualitative theory of Sturm-Liouville on spatial networks], Uspehi mat. nauk.2004. - V. 59, - P. 115-150.
[16] Znojil M. Quantum star-graph analogues of PT-symmetric square wells // Can. J. Phys. 2012 - V.90, iss 12. - P.1287-1293.
[17] Naimark M.A. Lineinye differenciyalnye operatory [Linear differential operators] - М.: Nauka. 1969. - P.526.
[18] F.Harary, Graph theory, Addison-Wesley Publishing Company. 1969. - 274 p.
[19] P. Kurasov, M. Garjiani, Quantum graphs: PT-symmetry and reflection symmetry of the spectrum.// Journal of Mathematical Physics. 2017. - V.58.
[20] M. Astudillo, P. Kurasov, M. Usman, RT -symmetric laplace operators on star graphs: Real spectrum and selfadjointness. // Adv. Math. Phys. 2015.
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Как цитировать
Rasa, G. H. A., Auzerkhan, G. S., & Konyrkulzhayeva, M. N. (2019). Функция Грина задачи Дирихле дифференциального оператора на графе - звезде при m. Вестник КазНУ. Серия математика, механика, информатика, 101(1), 14–28. https://doi.org/10.26577/JMMCS-2019-1-613
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