Журнал «Математические заметки СВФУ»最新文献

{"title":"PSEUDOPARABOLIC AND PSEUDOHYPERBOLIC EQUATIONS IN NONCYLINDRICAL TIME DOMAINS","authors":"А.И. Кожанов, Г.А. Лукина","doi":"10.25587/svfu.2019.17.12.002","DOIUrl":"https://doi.org/10.25587/svfu.2019.17.12.002","url":null,"abstract":"Исследована разрешимость новых краевых задач для псевдопараболических и псевдогиперболических дифференциальных уравнений с одной пространственной переменной. Отличительной особенностью этих задач является то, что их решения ищутся в нецилиндрических по временной переменной областях, а не в областях с криволинейными боковыми сторонами (областях с подвижной границей), как в других работах. Для изучаемых задач доказываются теоремы существования и единственности регулярных (имеющих во внутренних подобластях все обобщенные по С. Л. Соболеву производные, входящие в уравнение) решений.\u0000 We study solvability of new boundary value problems for pseudoparabolic and pseudohyperbolic equations with one spatial variable. The solutions for these problems are sought in domains noncylindrical along the time variable, not in the domains with curvilinear borders (domains with moving border) as in the previous works. We prove the existence and uniqueness theorems for the regular solutions, those having all generalized Sobolev derivatives, required in the equation, in the inner subdomains.","PeriodicalId":177207,"journal":{"name":"Журнал «Математические заметки СВФУ»","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131005749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"BOUNDARY CONTROL FOR PSEUDOPARABOLIC EQUATIONS IN SPACE","authors":"Z. Fayazova","doi":"10.25587/svfu.2019.20.57.008","DOIUrl":"https://doi.org/10.25587/svfu.2019.20.57.008","url":null,"abstract":"Let u(x, y, t) be a solution to the pseudoparabolic equation that satisfies the initial and boundary conditions. The value of the solution is given on the part of boundary of the considered region which contains the control parameter. It is required to choose the control parameter so that on a part of the regularity domain the solution takes the specified mean value. First, we consider an auxiliary boundary value problem for a pseudoparabolic equation. We prove the existence and uniqueness of the generalized solution from the corresponding class. The restriction for the admissible control is given in the integral form. By the separation variables method, the desired problem is reduced to the Volterra integral equation. The latter is solved by the Laplace transform method. The theorem on the existence of an admissible control is proved.","PeriodicalId":177207,"journal":{"name":"Журнал «Математические заметки СВФУ»","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123590107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ON DIMENSION OF THE SPACE OF KILLING FIELDS ON k–SYMMETRIC LORENTZIAN MANIFOLDS","authors":"Д.Н. Оскорбин, Е.Д. Родионов, И.В. Эрнст","doi":"10.25587/svfu.2019.19.57.004","DOIUrl":"https://doi.org/10.25587/svfu.2019.19.57.004","url":null,"abstract":"Исследованы поля Киллинга на kсимметрических лоренцевых многообразиях. Множество решений уравнения Киллинга образуют алгебру Ли киллинговых полей. Представленное исследование сфокусировано прежде всего на размерности этой алгебры. Рассмотренные лоренцевы многообразия, называемые обобщенными пространствами Кахена Уоллаха, имеют удобную систему локальных координат. В локальных координатах описано общее решение уравнения Киллинга на локально неразложимых 2симметрических лоренцевых многообразиях, которые являются обобщенными многообразиями Кахена Уоллаха, что было показано А. С. Галаевым и Д. В. Алексеевским. Дано явное описание всех возможных размерностей алгебры киллинговых полей на 2симметрических лоренцевых многообразиях малых размерностей.\u0000 We study the Killing equation on ksymmetric Lorentzian manifolds. Solutions of this equation form a Lie algebra called the algebra of Killing fields. Our consideration is focused primarily on the dimension of the Lie algebra of Killing fields. The Lorentzian manifolds we consider in this article are the generalized Cahen Wallach spaces, which are convinient to use because of the coordinate system they have. Using these coordinates, we describe the general solution of the Killing equation on locally indecomposable 2symmetric Lorentzian manifolds, which are generalized CahenWallach spaces, as was proved by A. S. Galaev and D. V. Alekseevsky. Finally, we give an explicit description of all possible dimensions of the algebra of Killing fields on 2symmetric Lorentzian manifolds of small dimensions.","PeriodicalId":177207,"journal":{"name":"Журнал «Математические заметки СВФУ»","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122007643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"DECONVOLUTION PROBLEM FOR INDICATORS OF SEGMENTS","authors":"Н.П. Волчкова, Вит.В. Волчков","doi":"10.25587/svfu.2019.47.12.001","DOIUrl":"https://doi.org/10.25587/svfu.2019.47.12.001","url":null,"abstract":"Пусть 1, . . . , n семейство распределений с компактными носителями на вещественной оси. Восстановление функции (распределения) f по известным сверткам f 1, . . . , f n называется деконволюцией. В работе рассматривается проблема деконволюции для n 2 и j rj , j 1, 2, где rj индикатор отрезка rj, rj. Эта задача является корректно поставленной лишь при условии несоизмеримости чисел r1 и r2. Основной результат работы дает формулу обращения оператора f (f r1, f r2) в указанном случае.\u0000 Let 1, . . . , n be a family of compactly supported distributions on real axis. Reconstruction of a function (distribution) f by given convolutions f 1, . . . , f n is called deconvolution. We consider the deconvolution problem for n 2 and j rj , j 1, 2, where rj is the indicator of segment rj, rj. This problem is correctly settled only under the condition of incommensurability of numbers r1 and r2. The main result of the article gives an inversion formula for the operator f (f r1, f r2) in the indicated case.","PeriodicalId":177207,"journal":{"name":"Журнал «Математические заметки СВФУ»","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129189020","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"PECULIARITIES OF THE DYNAMICS OF A BROWNIAN PARTICLE WITH RANDOM DISTURBANCES ORTHOGONAL TO ITS SPEED","authors":"В.А. Дубко","doi":"10.25587/svfu.2019.31.78.003","DOIUrl":"https://doi.org/10.25587/svfu.2019.31.78.003","url":null,"abstract":"Классические диффузионные уравнения основаны на предположении, что скорости броуновской частицы могут принимать сколь угодно большие значения. В статье показано, что для решения уравнения Ланжевена, когда случайные влияния ортогональны скорости частицы, может существовать притягивающая поверхность для скорости, несмотря на то, что процесс Винера это процесс, который принимает сколь угодно большие значения. В отличие от наших предыдущих статей и статей других исследователей, в этой статье построено уравнение для определения вероятности распределения частиц в координатном пространстве с учетом зависимости от начального направления скорости. Показано, что при определенном согласовании коэффициентов в исходном стохастическом уравнении небольшие случайные влияния приводят к описанию плотности вероятности положения частицы на основе волновых уравнений. Отмечено, что рассмотренные уравнения не исчерпывают класс моделей, когда возмущения ортогональны компоненте решения. Расширенный класс стохастических уравнений с ортогональными возмущениями рассматривался в предыдущих работах автора, в том числе для nмерных процессов, в связи с развитием теории первых интегралов для стохастических систем.\u0000 The classical diffusion equations are based on the assumption that the velocities of a Brownian particle can take arbitrarily large values. In this article, it is shown that for solving the Langevin equations when random influences are orthogonal to the particle velocity there might exist an attractive surface for velocity, despite the fact that the Wiener process is a process that takes arbitrarily large values. Unlike the previous articles, here we construct an equation for determining the probability density of the distribution of particles in the coordinate space taking the initial direction of velocity into account. It is shown that small influences with a certain agreement of the coefficients in the initial stochastic equation lead to a description of the moving particle based on the wave equations with constant speed. The considered equations do not exhaust the class of models when the perturbations are orthogonal to the vector component of the solution. An extended class of stochastic equations with orthogonal perturbations was considered in previous works of the author, in particular, for ndimensional processes, in connection with the development of the theory of first integrals for stochastic systems.","PeriodicalId":177207,"journal":{"name":"Журнал «Математические заметки СВФУ»","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131916439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ε–RETRACTS, Q–MANIFOLDS, AND FIXED POINTS","authors":"П.В. Черников","doi":"10.25587/svfu.2019.89.45.007","DOIUrl":"https://doi.org/10.25587/svfu.2019.89.45.007","url":null,"abstract":"Приводится обобщение одной теоремы Ногуши о неподвижной точке. Доказано, что существует компактное нестягиваемое ацикличное Qмногообразие, обладающее свойством неподвижной точки. Вводится и изучается понятие топологического пространства, обладающего свойством неподвижной точки. Приведен пример некомпактного множества на плоскости R2, обладающего свойством неподвижной точки.\u0000 A generalization of one of the Noguchi fixed point theorems is presented. We prove that there exists a compact noncollapsible acyclic Qmanifold with the fixed point property. A topological space with the fixed point property is introduced and studied and an example of a noncompact set in R2 with the fixed point property is given.","PeriodicalId":177207,"journal":{"name":"Журнал «Математические заметки СВФУ»","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115721457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"3D SIMULATION OF THE THERMAL REGIME OF A GROUP OF GAS WELLS IN THE SREDNETYUNGSKOE FIELD","authors":"V. A. Ivanov, P. Sivtsev, I. Rozhin","doi":"10.25587/SVFU.2019.26.34.009","DOIUrl":"https://doi.org/10.25587/SVFU.2019.26.34.009","url":null,"abstract":"The thermal interaction between a group of gas wells and the permafrost ground was simulated using the finite element method for the conditions of the Srednetyungskoe field. For the spacings between the wellheads of 10 m, 15 m, and 20 m, thermal regimes for the gas and surrounding ground massif are forecasted for 30 years of operation. The feature of the present work is that atmospheric conditions and the effect of the wells are modeled simultaneously in 3D, allowing for accurate characterization of the wellhead area. Field data on the ground temperature, the bottomhole pressure and temperature, the production rate, the gas composition, thermophysical properties of the ground, and weather conditions are used as input parameters. Temperature profiles of the ground, the position of the thawing front, and timing of merger of the thawing halos around the wells are estimated. The results of the survey can be used in development planning of the field.","PeriodicalId":177207,"journal":{"name":"Журнал «Математические заметки СВФУ»","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122299252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"SOME BOUNDARY VALUE PROBLEMS FOR THE SOBOLEV–TYPE OPERATOR–DIFFERENTIAL EQUATIONS","authors":"М.В. Уварова, С.Г. Пятков","doi":"10.25587/svfu.2019.70.19.006","DOIUrl":"https://doi.org/10.25587/svfu.2019.70.19.006","url":null,"abstract":"Рассматривается вопрос о разрешимости краевых задач для операторнодифференциального уравнения вида But Lu f, где B, L : X X (X банахово пространство) замкнутые операторы такие, что D(L) D(B) (D(L), D(B) области определения соответствующих операторов), с краевыми условиями Bu(0) Bu0 или TR0 Bu()d() Bu0, где функция ограниченной вариации. Уточняются некоторые известные результаты о разрешимости начальнокраевых задач для операторнодифференциальных уравнений типа Соболева в случае произвольного убывания (роста) резольвенты соответствующего линейного пучка. Получены теоремы о существовании и единственности решений задачи типа Коши и нелокальной краевой задачи общего вида, в том числе при определенных условиях показана максимальная регулярность решений. Последние результаты основаны на теореме Михлина для операторнозначных мультипликаторах Фурье. В отличие от предыдущих результатов в качестве функциональных пространств используются пространства Соболева Бесова.\u0000 We consider the solvability of boundary value problems for operatordifferential equation of the form But Lu f, where X is a Banach space, B, L : X X are closed operators such that D(L) D(B) (D(L), D(B) are domains of the corresponding operators), with boundary conditions Bu(0) Bu0 or R0T Bu()d() Bu0, where is a function of bounded variation. Some wellknown results on solvability of initial boundary value problems for operatordifferential equations of Sobolev type are refined in the case of arbitrary decrease (growth) of the resolvent of the corresponding linear pencil. Existence and uniqueness theorems of solutions to the Cauchytype problems and general nonlocal boundary value problems are obtained and the maximal regularity of solutions is proven under certain conditions. The results rely on Mikhlin theorems for operatorvalued Fourier multipliers. In contrast to the previous results, the function spaces are the Sobolev Besov spaces.","PeriodicalId":177207,"journal":{"name":"Журнал «Математические заметки СВФУ»","volume":"42 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130228633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Erratum and addendum to the paper “Weyl-almost periodic and asymptotically Weyl-almost periodic properties of solutions to linear and semilinear abstract Volterra integro-differential equations","authors":"M. Kostic","doi":"10.25587/svfu.2019.102.31520","DOIUrl":"https://doi.org/10.25587/svfu.2019.102.31520","url":null,"abstract":"The main aim of this paper is to perceive some inconsistencies made in the paper “Weyl-almost periodic and asymptotically Weyl-almost periodic properties of solutions to linear and semilinear abstract Volterra integro-differential equations”, recently published in Mathematical Notes of SVFU, as well as to propose alternative solutions for problems considered.","PeriodicalId":177207,"journal":{"name":"Журнал «Математические заметки СВФУ»","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128307105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ukhalov Properties of (0, 1)-matrices of order n having maximal determinant","authors":"M. Nevskii, A. Ukhalov","doi":"10.25587/svfu.2019.102.31516","DOIUrl":"https://doi.org/10.25587/svfu.2019.102.31516","url":null,"abstract":"We give some necessary conditions for the maximality of (0, 1)-determinant. Let M be a nondegenerate (0, 1)-matrix of order n. Denote by A the matrix of order n + 1 which is obtained from M by adding the (n + 1)th row (0, 0, . . . , 0, 1) and the (n + 1)th column consisting of 1’s. We prove that if A−1 = (li,j) then for all","PeriodicalId":177207,"journal":{"name":"Журнал «Математические заметки СВФУ»","volume":"12 9","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120839873","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}