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Устойчивость эволюционного линейного уравнения соболевского типа

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dc.contributor.author Москвичева, П.О.
dc.contributor.author Moskvicheva, P.O.
dc.date.accessioned 2020-02-26T06:39:50Z
dc.date.available 2020-02-26T06:39:50Z
dc.date.issued 2017
dc.identifier.citation Москвичева, П.О. Устойчивость эволюционного линейного уравнения соболевского типа / П.О. Москвичева // Вестник ЮУрГУ. Серия: Математика. Механика. Физика. 2017. Т. 9, № 3. С. 13-17. DOI: 10.14529/mmph170302. Moskvicheva P.O. Stability of the evolutionary linear Sobolev type equation. Bulletin of the South Ural State University. Series: Mathematics. Mechanics. Physics. 2017, vol. 9, no. 3, pp. 13-17. (in Russian). DOI: 10.14529/mmph170302 ru_RU
dc.identifier.issn 2075-809Х
dc.identifier.issn 2409-6547
dc.identifier.uri http://dspace.susu.ru/xmlui/handle/0001.74/27024
dc.description П.О. Москвичева, Южно-Уральский государственный университет, г. Челябинск, Российская Федерация E-mail: pelageia@bk.ru. P.O. Moskvicheva South Ural State University, Chelyabinsk, Russian Federation E-mail: pelageia@bk.ru ru_RU
dc.description.abstract Уравнения соболевского типа являются частью обширной области неклассических уравнений математической физики. Они возникают при моделировании различных процессов в естественных и технических науках. Исследуется устойчивость стационарного решения эволюционного уравнения, возникшего в теории фильтрации и заданного в ограниченной области. Для данного уравнения рассматривается начально-краевая задача. Получены условия, при которых нулевое решение уравнения устойчиво. Sobolev type equations are a part of extensive area of non-classical equations of mathematical physics. These are equations that are not solved respective to the highest derivative with respect to time. Research of different problems for equations of the given type nowadays are very relevant, as such equations appear during modeling of different processes in natural and engineering sciences. In this article, stability of stationary solution of an evolutionary equation, which appeared in the filter theory and which describes development of form of the filterable liquid’s free surface, is researched. For this equation, an initial boundary-value problem in limited area is considered. The article consists of an introduction, a list of references and two parts. In the first part, general concepts and theory assertions concerning p-sectorial operators are given. After that, reduction of the considered problem to the Cauchy problem for a Sobolev type abstract linear equation, by the means of selecting the corresponding Banach spaces and linear operators, is carried out. Then the phase space of our problem is described. In the second part, general concepts of the stability theory such as flow, stationary point of the flow, and Lyapunov functional, are given. Theorems of stability and asymptotical stability of a stationary point of the flow are given. In this article, the method of Lyapunov functional, modified for the case of complete normalized spaces, is used. It should be noted, that modification of the method lies in transition from incomplete normalized spaces to complete normalized spaces. As a result, the uniformity of stability and asymptotic stability is lost, but the class of problems being solved gets considerably expanded. The main result of the article are conditions formulated as a theorem of stability and asymptotic stability of zero solution of the considered 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 9
dc.subject УДК 517.9 ru_RU
dc.subject уравнение соболевского типа ru_RU
dc.subject относительно p-секториальные операторы ru_RU
dc.subject устойчивость ru_RU
dc.subject функционал Ляпунова ru_RU
dc.subject Sobolev type equations ru_RU
dc.subject relatively p-sectorial operators ru_RU
dc.subject stability ru_RU
dc.subject Lyapunov functional ru_RU
dc.title Устойчивость эволюционного линейного уравнения соболевского типа ru_RU
dc.title.alternative Stability of the evolutionary linear Sobolev type equation ru_RU
dc.type Article ru_RU
dc.identifier.doi DOI: 10.14529/mmph170302

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