Жойылатын облыста жылу өткiзгiштiктiң екi өлшемдi шекаралық есебiн шешу
DOI:
https://doi.org/10.26577/JMMCS.2021.v111.i3.06Кілттік сөздер:
цилиндрлiк емес облыс, конус, жылу өткiзгiштiктiң шекаралық есебi, Вольтерраның сингулярлық интегралдық теңдеуi, регуляризацияАннотация
Мақалада конустан тыс, яғни бастапқы уақытта нүктеге айналатын облыста жылу өткізгіштіктің шекаралық есебі қарастырылады. Мұндағы шекаралық шарт уақыт бойынша алынған туындыны қамтиды. Қарастырылып отырған есеп жылжымалы шекараның бар болуымен және бастапқы уақытта шешу облысының нүктеге айналуымен ерекшеленеді. Мұндай түрдегі есептерді жалпы жағдайда белгілі классикалық әдістермен шешуге болмайды. Бұл шекаралық есептер жылу потенциалдарының әдісімен екінші текті Вольтерр типіндегі сингулярлық интегралдық теңдеулерді шешуге келтіріледі. Вольтерр типіндегі сингулярлық теңдеуді ядросы келесі қасиетке ие болатын теңдеу деп түсіну керек: жоғарғы шек төменгі шекке ұмтылғанда ядродан алынған интеграл нөлге ұмтылмайды. Елеулі шенелген функциялар кеңістігінде қарастырылатын шекаралық есептің шешімділігі туралы теорема дәлелденді. Берілген есеп түрленетін екінші текті Вольтерр синугялрлық интегралдық теңдеудің шешімділігі туралы мәселелер зерттелді. Осы сингулярлық интегралдық теңдеудің нөлдік емес шешімі табылды.
Библиографиялық сілтемелер
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[15] Kavokin A.A., Kulakhmetova A.T., Shpadi Y.R. "Application of Thermal Potentials to the Solution of the Problem of Heat Conduction in a Region Degenerates at the Initial Moment" , Filomat, 132 (2018): 825-836.
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[19] Jenaliyev M.T., Ramazanov M.I. "On a Homogeneous Parabolic Problem in an Infinite Corner Domain" , Filomat, 32:3 (2018): 965-974.
[20] Baderko E.A. "Parabolic problems and boundary integral equations" , Mathematical methods in the applied sciences, 20 (1997): 449-459.
[21] Polianin A.D., Manzhirov A.V. Handbook of integral equations (Boca Raton, CRC Press, 2008).
[22] Gakhov F.D., Chersky Yu.I. Convolution type equations [Uravneniya tipa svyortki] (Moscow: Nauka, 1978).
[23] Prudnikov A.P., Brychkov Yu.A., Marichev O.I. Integrals and Series. Volume 2. Special Functions (Moscow: Fizmatlit, 2003).
[2] Kheloufi A., Sadallah B.-K. "On the regularity of the heat equation solution in non-cylindrical domains: Two approaches", Applied mathematics and computation, 218 (2011): 1623-1633.
[3] Kheloufi A. "Existence and uniqueness results for parabolic equations with Robin type boundary conditions in a non-regular domain of R3" , Applied mathematics and computation, 220 (2013): 756-769.
[4] Cherfaoui S., Kessab A., Kheloufi A. "Well-posedness and regularity results for a 2m-th order parabolic equation in symmetric conical domains of RN+1" , Mathematical methods in the applied sciences, 40:5 (2017): 6035-6047.
[5] Kheloufi A. "On a Fourth Order Parabolic Equation in a Nonregular Domain of R3" , Mediterranean journal of mathematics, 12 (2014): 803-820.
[6] Kheloufi A., Sadallah B.-K. "Study of the heat equation in a symmetric conical type domain of RN+1" , Mathematical methods in the applied sciences, 37 (2014): 1807-1818.
[7] Chapko R., Johansson B.T., Vavrychuk V. "Numerical solution of parabolic Cauchy problems in planar corner domains", Mathematics and computers in simulation, 101 (2014): 1-12.
[8] Wang Y., Huang J., Wen X. "Two-dimensional Euler polynomials solutions of two-dimensional Volterra integral equations of fractional order" , Applied numerical mathematics, 163 (2021): 77-95.
[9] Dehbozorgi R., Nedaiasl K. "Numerical solution of nonlinear weakly singular Volterra integral equations of the first kind: An hp-version collocation approach" , Applied numerical mathematics, 161 (2021): 111-135.
[10] Wisniewski G., Habrych M., Miedzinski B. "Approach to prediction the transition of a small power low voltage switching arc into glowing" , 20th International Symposium on Electrical Apparatus and Technologies (SIELA), 3-6 June 2018, Bourgas, Bulgaria, Danvers, MA: IEEE.
[11] Miedzinski B., Wisniewski G., Kharin S.N., Nouri H., Grechanyuk M. "Arc-to-glow transition approachforpracticalusein dc low-power, low-voltageelectricgrids" , IEEE Transactions on Components Packagingand Manufacturing Technology, 8:6 (2018): 932-938.
[12] Kharin S.N., Nouri H., Miedzinski B., Wisniewski G. "Transient phenomena of arc to glow discharge transformation at contact opening" , Proc. of 21st Int. Conf. on Electric contacts, Zurich, Switzerland, (2002): 425-431.
[13] Kharin S. "Mathematical model of electrical contact bouncing" , AIP Conference Proceedings, (2015): 1676.
[14] Sarsengeldin M.M., Kharin S.N., Rayev Z., Khairullin Y. "Mathematical model of heat transfer in opening electrical contacts with tunnel effect" , Filomat, 32 (2018): 1003-1008.
[15] Kavokin A.A., Kulakhmetova A.T., Shpadi Y.R. "Application of Thermal Potentials to the Solution of the Problem of Heat Conduction in a Region Degenerates at the Initial Moment" , Filomat, 132 (2018): 825-836.
[16] Amangalieva M.M., Akhmanova D.M., Dzhenaliev M.T., Ramazanov M.I. "Boundary value problems for a spectrally loaded heat operator with load line approaching the time axis at zero or infinity" , Differential Equations, 47:2 (2011): 231-243.
[17] Jenaliyev M.T., Amangaliyeva M.M., Kosmakova M.T., Ramazanov M.I. "On a Volterra equation of the second kind with incompressible kernel" , Advances in Difference Equations, 2015 (2015): article number 71.
[18] Amangalieva M.M., Dzhenaliev M.T., Kosmakova M.T., Ramazanov M.I. "On one homogeneous problem for the heat equation in an infinite angular domain" , Siberian Mathematical Journal, 56:6 (2015): 982-995.
[19] Jenaliyev M.T., Ramazanov M.I. "On a Homogeneous Parabolic Problem in an Infinite Corner Domain" , Filomat, 32:3 (2018): 965-974.
[20] Baderko E.A. "Parabolic problems and boundary integral equations" , Mathematical methods in the applied sciences, 20 (1997): 449-459.
[21] Polianin A.D., Manzhirov A.V. Handbook of integral equations (Boca Raton, CRC Press, 2008).
[22] Gakhov F.D., Chersky Yu.I. Convolution type equations [Uravneniya tipa svyortki] (Moscow: Nauka, 1978).
[23] Prudnikov A.P., Brychkov Yu.A., Marichev O.I. Integrals and Series. Volume 2. Special Functions (Moscow: Fizmatlit, 2003).
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Как цитировать
Ramazanov, M. I., & Gulmanov, N. K. (2021). Жойылатын облыста жылу өткiзгiштiктiң екi өлшемдi шекаралық есебiн шешу. Қазұу Хабаршысы. Математика, механика, информатика сериясы, 111(3), 65–78. https://doi.org/10.26577/JMMCS.2021.v111.i3.06
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