Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki最新文献_第7页

Inverse image of precompact sets and regular solutions to the Navier–Stokes equations 预紧集的逆像与Navier-Stokes方程的正则解

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-06-01 DOI: 10.35634/vm220208

Shlapunov A.A., Tarkhanov N.N.

引用次数: 0

On the solvability of nonlocal initial-boundary value problems for a partial differential equation of high even order 高偶阶偏微分方程非局部初边值问题的可解性

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-06-01 DOI: 10.35634/vm220206

Urinov A.K., Azizov M.S.

{"title":"On the solvability of nonlocal initial-boundary value problems for a partial differential equation of high even order","authors":"Urinov A.K., Azizov M.S.","doi":"10.35634/vm220206","DOIUrl":"https://doi.org/10.35634/vm220206","url":null,"abstract":"In the present paper, two non-local initial-boundary value problems have been formulated for a partial differential equation of high even order with a Bessel operator in a rectangular domain. The correctness of one of the considered problems has been investigated. To do this, applying the method of separation of variables to the problem under consideration, the spectral problem was obtained for an ordinary differential equation of high even order. The self-adjointness of the last problem was proved, which implies the existence of the system of its eigenfunctions, as well as orthonormality and completeness of this system. Further, the Green's function of the spectral problem was constructed, with the help of which it was equivalently reduced to the Fredholm integral equation of the second kind with symmetrical kernel. Using this integral equation and Mercer's theorem, the uniform convergence of some bilinear series depending on found eigenfunctions has been studied. The order of the Fourier coefficients was established. The solution of the considered problem has been written as the sum of a Fourier series with respect to the system of eigenfunctions of the spectral problem. The uniform convergence of this series and also the series obtained from it by term-by-term differentiation was proved. Using the method of spectral analysis, the uniqueness of the solution of the problem was proved. An estimate for the solution of the problem was obtained, from which its continuous dependence on the given functions follows.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80216452","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}

引用次数: 1

On the exo-planet precession under torqes due to three celestial bodies with the evolution of the satellite's orbit 在系外行星进动下，由于三颗天体的转矩随卫星轨道的演化而变化

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-06-01 DOI: 10.35634/vm220210

Krasil'nikov P.S.

{"title":"On the exo-planet precession under torqes due to three celestial bodies with the evolution of the satellite's orbit","authors":"Krasil'nikov P.S.","doi":"10.35634/vm220210","DOIUrl":"https://doi.org/10.35634/vm220210","url":null,"abstract":"We investigate the non-resonant evolution of the axial tilt of hypothetical exo-Earth in the gravitational field of a star, planet's satellite (exo-Moon) and outer planet (exo-Jupiter). The exo-Earth is assumed to be rigid, axially symmetric ($A=B$) and almost spherical. We assume the orbits of the both exo-planets to be Keplerian ellipses with focus in the star, the orbit of exo-Moon to be an evolving Keplerian ellipse with slowly changing of ascending node longitude and periapsis argument.\u0000Assuming the frequencies of the unperturbed orbital elliptical motion to be of the order of unity, we obtain the canonical averaged equations describing the perturbed oscillations of the exo-Moon spin axis. These equations contain parameters changing slowly over time. Using the smallness of the planets' masses relative to the mass of the star, we have obtained simplified equations of oscillations of the exo-Earth spin axis by the small parameter method. Time integration of simplified equations gives the axial tilt of exo-Moon as a function of time. It is shown that the torques from the exo-Jupiter create a secular, long-period oscillation mode in axial tilt with a frequency equals to frequency of unperturbed spin axis precession of the exo-Earth. The impact of the exo-Moon on the evolution of the exo-Earth spin axis is that short-period harmonics appear in the oscillations of the axial tilt. The frequency of such oscillations is close to the precession frequency of the ascending node longitude of the exo-Moon orbit.\u0000We have calculated the evolution of exo-Earth axial tilt for two exo-planetary systems, i.e., for a system similar to the solar system, and for a planetary exo-system 7 Canis Majoris. The effect of destabilization (stabilization) of the exo-Earth tilt oscillations due to the torques exerted by exo-Moon and exo-Jupiter is described.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76405494","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}

引用次数: 0

Vector fields with zero flux through circles of fixed radius on $mathbb{H}^2$ $mathbb{H}^2$上通过固定半径圆的零通量向量场

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-03-01 DOI: 10.35634/vm220101

N. Volchkova, V. Volchkov

引用次数: 0

On local extension of the group of parallel translations in three-dimensional space 三维空间中平行平移群的局部扩展

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-03-01 DOI: 10.35634/vm220105

V. Kyrov

引用次数: 0

On uniform convergence of approximations of the double layer potential near the boundary of a two-dimensional domain 二维域边界附近双层势近似的一致收敛性

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-03-01 DOI: 10.35634/vm220103

D. Ivanov

引用次数: 0

On totally global solvability of evolutionary equation with monotone nonlinear operator 单调非线性算子演化方程的全局可解性

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-03-01 DOI: 10.35634/vm220109

A. Chernov

{"title":"On totally global solvability of evolutionary equation with monotone nonlinear operator","authors":"A. Chernov","doi":"10.35634/vm220109","DOIUrl":"https://doi.org/10.35634/vm220109","url":null,"abstract":"x +Ax = f [u](x), x(0) = a ∈ H; x ∈ W = {x ∈ X : x ∈ X}, где u ∈ U — управление, f [u] : C(0, T ;H) → X∗ — вольтерров оператор (W ⊂ C(0, T ;H)), доказана тотально (по множеству допустимых управлений) глобальная разрешимость при условии глобальной разрешимости некоторого функционально-интегрального неравенства в пространстве R. Во многих частных случаях указанное неравенство может быть конкретизировано как задача Коши для обыкновенного дифференциального уравнения. Фактически, развивается аналогичный результат, доказанный автором ранее для случая линейного оператора A и V = H = V ∗. Отдельно рассматриваются случаи компактного вложения пространств, усиления условия монотонности и совпадения тройки пространств V = H = H∗. В последних двух случаях доказывается также единственность решения. В первом случае применяется теорема Шаудера, в остальных — технология продолжения решения по времени (то есть продолжения вдоль вольтерровой цепочки). Приводятся конкретные примеры задания оператора A.","PeriodicalId":43239,"journal":{"name":"Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87363682","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}

引用次数: 0

Group pursuit in a problem with fractional derivatives in the class of positional strategies with a guide 一类带向导的位置策略中带有分数阶导数问题的群追

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-03-01 DOI: 10.35634/vm220107

N. Petrov, A. I. Machtakova

引用次数: 0

Weakly invo-clean rings having weak involution 具有弱对合的弱对合环

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-03-01 DOI: 10.35634/vm220102

P. Danchev

引用次数: 0

Pauli's theorem in Clifford algebras of odd dimension 奇维Clifford代数中的泡利定理

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Vestnik Udmurtskogo Universiteta-Matematika Mekhanika Kompyuternye Nauki Pub Date : 2022-03-01 DOI: 10.35634/vm220104

S. P. Kuznetsov, V. Mochalov, V. Chuev

引用次数: 0