БЕЙЛОКАЛ ПУАССОН ТЕҢДЕУІ ҮШІН ПЕРИОДТЫ ШЕТТІК ЕСЕПТЕР ТУРАЛЫ
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Кілт сөздер:
инволюция, бейлокал оператор, Пуассон теңдеуі, Лаплас операторы, периодтық есеп, Дирихле есебі, Нейман есебі, меншікті функциялар, меншікті мәндер.Аңдатпа
Бұл жұмыста бірлік шарда аргументтері түрлендірілген шеттік есептер зерттеледі. Аргументтерді түрлендіру инволюция түріндегі бейнелер арқылы беріледі. Бұл бейнелелер теңдеуге де, шеттік шарттарда да қатысады. Қарастырылып отырған теңдеу Пуассон теңдеуінің бейлокал аналогы болып табылады. Шеттік шарттар ізделінді функцияның шардың жоғарғы жарты бөлігіндегі мәнімен төменгі жарты шардағы мәнімен байланыстыру түрінде беріледі. Бұл шарттар әйгілі периодты шарттарды шар түріндегі аймақтар үшін жалпылайды. Шеттік есептерді зерттеу кезінде инволюциялық түрлендірулердің қасиеттері қолданылады. Қарастырылып отырған есептер оларды классикалық Пуассон теңдеуі үшін периодтық шарттармен берілген шеттік есептердің аналогтарына келтіру арқылы шешіледі. Қарастырылып отырған есептер үшін периодты белгілі нәтижелерді қолдана отырып, шешімнің бар және жалғыз болуы туралы теоремалар дәлелденді. Зерттелетін есептердің шешімділігінің дәл шарттары табылды. Периодты есептермен байланысты спектрлік мәселелер де зерттелді. Осы есептердің меншікті функциялары мен меншікті мәндері табылды.
Әдебиеттер тізімі
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Sadybekov M.A., Turmetov B.Kh. On an analog of periodic boundary value problems for the Poisson equation in the disk // Differential Equations. – 2014. – Vol. 50, No. 2. – P. 268 – 273. https://doi.org/10.1134/S0012266114020153.
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Sadybekov M.A., Dukenbayeva A.A. On a nonlocal boundary value problem for the Laplace operator, which is a multidimensional generalisation of the Samarskii-Ionkin problem // News of the Khoja Akhmet Yassawi KazakhTurkish international university. Mathematics, physics, computer science. – 2018. – Vol. 1, №1(4). – P. 81–83.
Sadybekov M.A., Dukenbayeva A.A. Direct and inverse problems for the Poisson equation with equality of flows on a part of the boundary // Complex Variables and Elliptic Equations. – 2019. – Vol. 64, №5. – P. 777-791. https://doi.org/10.1080/17476933.2018.1517340
Sadybekov M.A., Dukenbayeva A.A. On boundary value problem of the Samarskii-Ionkin type for the Laplace operator in a ball // Kazakh Mathematical Journal. – 2020. – Vol. 20, №1. – P. 84–94.
Sadybekov M.A., Dukenbayeva A.A. On boundary value problem of the Samarskii-Ionkin type for the Laplace operator in a ball // Complex Variables and Elliptic Equations. – 2022.– Vol. 67, № 2 – P. 369–383. https://doi.org/10.1080/17476933.2020.1828377
Sadybekov M.A., Turmetov B.Kh., Torebek B.T. Solvability of nonlocal boundary-value problems for the Laplace equation in the ball // Electronic Journal of Differential Equations. – 2014. – Vol. 2014, No. 157. – P. 1–14.
Sadybekov M.A., Yessirkegenov N.A. On a generalised SamarskiiIonkin type problem for the Poisson equation // Kazakh Mathematical Journal. – 2017. – Vol. 17, No. 1. – P. 115–116.
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Kal’menov T.S., Iskakova U.A. A criterion for the strong solvability of the mixed Cauchy problem for the Laplace equation // Dokl Math. – 2007. – Vol. 75, No. 3. – P. 370-373. https://doi.org/10.1134/S1064562407030118
Kal’menov T.S., Iskakova U.A. A method for solving the Cauchy problem for the Laplace equation // Dokl Math. – 2008. – Vol. 78, No. 3. – P. 874-876. https:// doi: 10.1134/S1064562408060185
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