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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki最新文献

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Investigation of conditions for preserving global solvability of operator equations by means of comparison systems in the form of functional-integral equations in $mathbf{C}[0;T]$ 通过$mathbf{C}[0;T]$中函数积分方程形式的比较系统探究保持算子方程全局可解性的条件
Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki Pub Date : 2024-03-01 DOI: 10.35634/vm240108
A.V. Chernov
{"title":"Investigation of conditions for preserving global solvability of operator equations by means of comparison systems in the form of functional-integral equations in $mathbf{C}[0;T]$","authors":"A.V. Chernov","doi":"10.35634/vm240108","DOIUrl":"https://doi.org/10.35634/vm240108","url":null,"abstract":"Let $U$ be the set of admissible controls, $T>0$ and it be given a scale of Banach spaces $W[0;tau]$, $tauin(0;T]$, such that the set of constrictions of functions from $W=W[0;T]$ to a closed segment $[0;tau]$ coincides with $W[0;tau]$; $F[cdot;u]colon Wto W$ be a controlled Volterra operator, $uin U$. For the operator equation $x=F[x;u]$, $xin W$, we introduce a comparison system in the form of functional-integral equation in the space $mathbf{C}[0;T]$. We establish that, under some natural hypotheses on the operator $F$, the preservation of the global solvability of the comparison system pointed above is sufficient to preserve (under small perturbations of the right-hand side) the global solvability of the operator equation. This fact itself is analogous to some results which were obtained by the author earlier. The central result of the paper consists in a set of signs for stable global solvability of functional-integral equations mentioned above which do not use hypotheses similar to local Lipschitz continuity of the right-hand side. As a pithy example of special interest, we consider a nonlinear nonstationary Navier–Stokes system in the space $mathbb{R}^3$.","PeriodicalId":517627,"journal":{"name":"Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki","volume":"107 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140406864","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
On the uniqueness of a solution to the multiplicative control problem for the electron drift–diffusion model 论电子漂移扩散模型乘法控制问题解的唯一性
Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki Pub Date : 2024-03-01 DOI: 10.35634/vm240101
© Р. В. Бризицкий, Н. Н. Максимова, R. Brizitskii, Nadezhda Nikolaevna Maksimova
{"title":"On the uniqueness of a solution to the multiplicative control problem for the electron drift–diffusion model","authors":"© Р. В. Бризицкий, Н. Н. Максимова, R. Brizitskii, Nadezhda Nikolaevna Maksimova","doi":"10.35634/vm240101","DOIUrl":"https://doi.org/10.35634/vm240101","url":null,"abstract":"The multiplicative control problem for a stationary diffusion-drift model of charging a polar dielectric is studied. The role of control is played by a leading coefficient in the model equation, which has the meaning of the electron diffusion coefficient. The global solvability of the boundary value problem and the local uniqueness of its solution, as well as the solvability of the extremum problem under consideration, have been proved in the previous papers of the authors. In this paper, an optimality system is derived for the control problem and local regularity conditions for the Lagrange multiplier are established. Based on the analysis of this system, the local uniqueness of the multiplicative control problem's solution for specific cost functionals is proved.","PeriodicalId":517627,"journal":{"name":"Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki","volume":"290 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140286854","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
On two problems of pursuit of a group of evaders in differential games with fractional derivatives 论分数导数微分博弈中追逐一组逃避者的两个问题
Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki Pub Date : 2024-03-01 DOI: 10.35634/vm240105
A. I. Machtakova, N.N. Petrov
{"title":"On two problems of pursuit of a group of evaders in differential games with fractional derivatives","authors":"A. I. Machtakova, N.N. Petrov","doi":"10.35634/vm240105","DOIUrl":"https://doi.org/10.35634/vm240105","url":null,"abstract":"In a finite-dimensional Euclidean space, the problem of pursuit of a group of evaders by a group of pursuers is considered, described by a system of the form\u0000begin{gather*}\u0000D^{(alpha)}x_i = a_i x_i + u_i, u_i in U_i, quad D^{(alpha)}y_j = b_jy_j + v, vin V,\u0000end{gather*}\u0000where $D^{(alpha)}f$ is the Caputo derivative of order $alpha$ of the function $f$. The sets of admissible controls $U_i, V$ are convex compacts, $a_i, b_j$ are real numbers. The terminal sets are convex compacts. Sufficient conditions for the solvability of the pursuit problems are obtained. In the study, the method of resolving functions is used as the basic one. It is shown that such a conflict situation with equal opportunities for all participants is possible, in which one pursuer catches all the evaders.","PeriodicalId":517627,"journal":{"name":"Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki","volume":"72 7","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140406239","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
Approximation by Nörlund type means in the grand Lebesgue spaces with variable exponent 在具有可变指数的大勒贝格空间中用诺尔隆德式方法逼近
Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki Pub Date : 2024-03-01 DOI: 10.35634/vm240102
S. Jafarov
{"title":"Approximation by Nörlund type means in the grand Lebesgue spaces with variable exponent","authors":"S. Jafarov","doi":"10.35634/vm240102","DOIUrl":"https://doi.org/10.35634/vm240102","url":null,"abstract":"In the present paper the approximation of functions by Nörlund type means in the generalized grand Lebesgue spaces with variable exponent is studied.","PeriodicalId":517627,"journal":{"name":"Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki","volume":"12 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140405466","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
Multi-pursuer pursuit differential game for an infinite system of second order differential equations 无穷二阶微分方程系统的多追求者追求微分博弈
Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki Pub Date : 2024-03-01 DOI: 10.35634/vm240104
R.Yu. Kazimirova, G.I. Ibragimov, R. M. Hasim
{"title":"Multi-pursuer pursuit differential game for an infinite system of second order differential equations","authors":"R.Yu. Kazimirova, G.I. Ibragimov, R. M. Hasim","doi":"10.35634/vm240104","DOIUrl":"https://doi.org/10.35634/vm240104","url":null,"abstract":"We study a pursuit differential game of many pursuers and one evader. The game is described by the infinite systems of $m$ inertial equations. By definition, pursuit in the game is completed if the state and its derivative of one of the systems are equal to zero at some time. In the literature, such a condition of completion of pursuit is also called soft landing. We obtain a condition in terms of energies of players which is sufficient for completion of pursuit in the game. The pursuit strategies are also constructed.","PeriodicalId":517627,"journal":{"name":"Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki","volume":"72 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140407344","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
Numerical solution of a control problem for a parabolic system with disturbances 带干扰抛物线系统控制问题的数值解法
Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki Pub Date : 2024-03-01 DOI: 10.35634/vm240103
I. Izmest'ev, V. Ukhobotov, K.N. Kudryavtsev
{"title":"Numerical solution of a control problem for a parabolic system with disturbances","authors":"I. Izmest'ev, V. Ukhobotov, K.N. Kudryavtsev","doi":"10.35634/vm240103","DOIUrl":"https://doi.org/10.35634/vm240103","url":null,"abstract":"A controlled parabolic system that describes the heating of a given number of rods is considered. The density functions of the internal heat sources of the rods are not known exactly, and only the segments of their change are given. At the ends of the rods there are controlled heat sources and disturbances. The goal of the choice of control is to lead the vector of average temperatures of the rods at a fixed time to a given compact for any admissible functions of the density of internal heat sources and any admissible realizations of disturbances. After replacing variables, the problem of controlling a system of ordinary differential equations in the presence of uncertainty is obtained. Using a numerical method, a solvability set is constructed for this problem. Model calculations are carried out.","PeriodicalId":517627,"journal":{"name":"Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki","volume":"56 20","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140400145","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
On stationary random processes with fuzzy states 关于具有模糊状态的静止随机过程
Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki Pub Date : 2024-03-01 DOI: 10.35634/vm240107
V. L. Khatskevich
{"title":"On stationary random processes with fuzzy states","authors":"V. L. Khatskevich","doi":"10.35634/vm240107","DOIUrl":"https://doi.org/10.35634/vm240107","url":null,"abstract":"In this paper, continuous random processes with fuzzy states are studied. The properties of their numerical characteristics – fuzzy expectations, expected values and covariance functions – are established. The main attention is paid to the class of stationary fuzzy-random processes. For them, the ergodicity property and the spectral representation of covariance function (generalized Wiener–Khinchin theorem) are substantiated. The results obtained are based on the properties of fuzzy-random variables and numerical random processes. Triangular fuzzy-random processes are considered as examples.","PeriodicalId":517627,"journal":{"name":"Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki","volume":"6 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140404102","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
Modeling of heat and mass transfer in the discontinuum approximation 非连续近似的传热和传质模型
Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki Pub Date : 2024-03-01 DOI: 10.35634/vm240109
S.I. Martynenko
{"title":"Modeling of heat and mass transfer in the discontinuum approximation","authors":"S.I. Martynenko","doi":"10.35634/vm240109","DOIUrl":"https://doi.org/10.35634/vm240109","url":null,"abstract":"The article presents a theoretical analysis of the governing equations expressing the fundamental conservation laws in the continuum and discontinuum approximations, and methods for solving problems of hydrodynamics as one of the most important subfields of continuum mechanics. This article is an attempt to more accurately describe physicochemical macro-processes. It is shown that the most suitable equations for computer modeling are the conservation laws under natural constraints on the minimum spatial and time scales, i.e., equations without partial derivatives and constraints on the solution smoothness. Using the continuity and thermal conductivity equations, a phenomenological method for constructing and numerically solving the governing equations is presented, and comparison with the traditional approach is given.","PeriodicalId":517627,"journal":{"name":"Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki","volume":"313 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140402524","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
Measures of stability and instability of the differential system zero solution and their dependence on the initial moment 微分系统零解的稳定性和不稳定性度量及其与初始矩的关系
Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki Pub Date : 2024-03-01 DOI: 10.35634/vm240106
I. N. Sergeev
{"title":"Measures of stability and instability of the differential system zero solution and their dependence on the initial moment","authors":"I. N. Sergeev","doi":"10.35634/vm240106","DOIUrl":"https://doi.org/10.35634/vm240106","url":null,"abstract":"The recently introduced concepts of stability measures and instability measures of different types are studied: Lyapunov, Perron or upper-limit. These concepts allow a natural probabilistic interpretation, which shows the dependence of specific properties of solutions of a differential system, starting close to its zero solution, on arbitrarily small perturbations of the initial values of the Cauchy problem with a fixed initial moment. The work examines precisely the dependence of these measures on the initial moment. It has been proved that this dependence is completely absent for one-dimensional and autonomous systems, as well as for many types of stability or instability of linear systems. Moreover, it has been proved that the extreme values of the measures of stability or instability themselves are always invariant with respect to the choice of the initial moment. Finally, an example of a system is given for which this dependence, on the contrary, manifests itself to the maximum possible extent.","PeriodicalId":517627,"journal":{"name":"Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki","volume":"67 S1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140407404","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
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