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Об одной задаче типа Дирихле для уравнения составного типа

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dc.contributor.author Зикиров, О.С.
dc.contributor.author Zikirov, O.S.
dc.date.accessioned 2020-02-18T10:12:10Z
dc.date.available 2020-02-18T10:12:10Z
dc.date.issued 2016
dc.identifier.citation Зикиров, О.С. Об одной задаче типа Дирихле для уравнения составного типа / О.С. Зикиров // Вестник ЮУрГУ. Серия: Математика. Механика. Физика. 2016. Т. 8, № 2. С. 19-26. DOI: 10.14529/mmph160203. Zikirov O.S. On a Dirichlet problem for composite type equation. Bulletin of the South Ural State University. Series: Mathematics. Mechanics. Physics. 2016, vol. 8, no. 2, pp. 19-26 (in Russian). DOI: 10.14529/mmph160203 ru_RU
dc.identifier.issn 2075-809Х
dc.identifier.issn 2409-6547
dc.identifier.uri http://dspace.susu.ru/xmlui/handle/0001.74/26978
dc.description О.С. Зикиров, Национальный университет Узбекистана, Ташкент, Узбекистан E-mail: zikirov@yandex.com. O.S. Zikirov, National University of Uzbekistan, Tashkent, Uzbekistan E-mail: zikirov@yandex.com ru_RU
dc.description.abstract Исследуется краевая задача для класса уравнений третьего порядка составного типа с эллиптическим оператором в главной части. Доказаны теоремы существования и единственности классического решения для рассматриваемых задач. Доказательство основано на энергетических неравенствах и на теории интегральных уравнений фредгольмовского типа. The aim of this paper is to prove the existence and uniqueness of smooth solutions to the Dirichlet type problem for one class of third-order equations that do not belong to any of the classic types. One of the main classes of non-classical equations is third-order composite type equations, the operator of which is a composition of first-order hyperbolic operator and an elliptic operator in the main part. A number of boundary value problems for the model composite type equations with the Laplace operator were investigated by T.D. Dzhuraev. Many studies have proved the existence of solutions to boundary value problems upon fulfillment of conditions of the convexity of area boundary. The method of proof used in this paper is similar to the method used in the research paper of the author mentioned above. For the research of composite type linear equations a combination of the method of potentials (Green's function) and integral identities is applied. The research method is based on reducing the studied problem with the help of the Green's function to an integral equation, the proof of its solubility and thus - the proof of the solvability of original problem. Upon fulfillment of certain conditions on given functions, a third-order equation reduces to a second-order equation of elliptic type with an unknown right-hand side and the boundary function. With the help of Green's functions for elliptic equations, the studied problem is reduced to a second-order equivalent integral equation, the solvability follows from Fredholm alternative and the theorem of uniqueness of the solution of the original problem. ru_RU
dc.language.iso other ru_RU
dc.publisher Издательский центр ЮУрГУ ru_RU
dc.relation.ispartof Вестник ЮУрГУ. Серия Математика. Механика. Физика
dc.relation.ispartof Vestnik Ûžno-Ural’skogo gosudarstvennogo universiteta. Seriâ Matematika. Mehanika. Fizika
dc.relation.ispartof Bulletin of SUSU
dc.relation.ispartofseries Математика. Механика. Физика;Том 8
dc.subject УДК 517.956 ru_RU
dc.subject краевые задачи ru_RU
dc.subject уравнения составного типа ru_RU
dc.subject оператор Лапласа ru_RU
dc.subject функция Грина ru_RU
dc.subject уравнения третьего порядка ru_RU
dc.subject интегралы энергии ru_RU
dc.subject задача Дирихле ru_RU
dc.subject интегральные уравнения ru_RU
dc.subject Boundary value problem ru_RU
dc.subject composite type equations ru_RU
dc.subject Laplace operator ru_RU
dc.subject Green’s function ru_RU
dc.subject third-order equations ru_RU
dc.subject energy integrals ru_RU
dc.subject Dirichlet problem ru_RU
dc.subject integral equations ru_RU
dc.title Об одной задаче типа Дирихле для уравнения составного типа ru_RU
dc.title.alternative On a Dirichlet problem for composite type equation ru_RU
dc.type Article ru_RU
dc.identifier.doi DOI: 10.14529/mmph160203


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