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Advances in Differential Equations and Control Processes最新文献

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Dynamics of Technological Development: Innovation, Imitation, Depreciation 技术发展动力学:创新、模仿、贬值
IF 0.1
Advances in Differential Equations and Control Processes Pub Date : 2023-01-01 DOI: 10.21638/11701/spbu35.2023.201
A. Kirillov, A. Sazonov
{"title":"Dynamics of Technological Development: Innovation, Imitation, Depreciation","authors":"A. Kirillov, A. Sazonov","doi":"10.21638/11701/spbu35.2023.201","DOIUrl":"https://doi.org/10.21638/11701/spbu35.2023.201","url":null,"abstract":"The nonlinear dynamical system, describing the dynamics of sector capital distribution over two levels of technological development, low and high, proposed. The dynamics is determined by the interaction of innovation and imitation process with the process of depreciation taking into account. The qualitative behavior of the system trajectories depending on the relationship of parameters determining the rates of innovation, imitation and depreciation processes is studied. The invariant set which all trajectories enter in a finite time is found. In the case of nonzero rate of innovation process, the uniqueness of equilibrium is proved. On the basis of proposed constructive geometrical method the sufficient conditions of its global stability are obtained. In order to study the behavior of isoclines the special curve parametrization, connected with the invariant set geometry, is proposed. It is shown that in the absence of innovation process the existence of two equilibria, stable and unstable, is possible. In addition, the transition to a high technological level, corresponding to a stable equilibrium, may not occur even under sufficiently small depreciation process rate. The bifurcation value of the imitation rate parameter is found.","PeriodicalId":41162,"journal":{"name":"Advances in Differential Equations and Control Processes","volume":"14 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87324548","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
Identification of Collector Properties of Relaxational-deformable Gas Stratum Based on the Development History Data 基于开发历史资料的松弛-变形气藏集热器性质识别
IF 0.1
Advances in Differential Equations and Control Processes Pub Date : 2023-01-01 DOI: 10.21638/11701/spbu35.2023.101
{"title":"Identification of Collector Properties of Relaxational-deformable Gas Stratum Based on the Development History Data","authors":"","doi":"10.21638/11701/spbu35.2023.101","DOIUrl":"https://doi.org/10.21638/11701/spbu35.2023.101","url":null,"abstract":"Improvement of efficiency of oil and gas reservoir development is directly connected with the reliability of the implemented development project, characterized by its full adequacy to the reservoir conditions. Such adequacy in designing the development of oil and gas reservoirs is most often ensured by providing comprehensive informativeness of the implemented reservoir hydrogasdynamic model, even with insufficient information about the physical and geological characteristics of the model. Due to the great diversity of these characteristics that directly affect development indicators, and the need to know them during the reservoir development process, the said adequacy of the implemented development project is established by using the effective algorithms, which maximally take into account these aspects of providing comprehensive informativeness of the implemented reservoir hydrogasdynamic model, one of which is the identification algorithm. The implementation of this algorithm can identify the physical and geological characteristics of the reservoir system hydrogasdynamic model being implemented, using the reservoir development data for the previous periods (according to the development history). In view of the above, the article proposes a method for identification of filtration-capacitative parameters of the relaxation-deformed reservoir based on the model of real gas filtration in the gas mode, using data from the development history. This technique makes it possible to simulate changes (to carry out identified determination) of permeability and porosity in all points of the relaxation-deformable gas reservoir, as well as to obtain a corresponding gas-dynamic predictive model of development.","PeriodicalId":41162,"journal":{"name":"Advances in Differential Equations and Control Processes","volume":"17 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81062002","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 Discontinuity of Extreme Exponents of Oscillation on a Set of Linear Homogeneous Differential Systems 一类线性齐次微分系统振荡极值指数的不连续性
IF 0.1
Advances in Differential Equations and Control Processes Pub Date : 2023-01-01 DOI: 10.21638/11701/spbu35.2023.106
{"title":"On the Discontinuity of Extreme Exponents of Oscillation on a Set of Linear Homogeneous Differential Systems","authors":"","doi":"10.21638/11701/spbu35.2023.106","DOIUrl":"https://doi.org/10.21638/11701/spbu35.2023.106","url":null,"abstract":"In this paper, we study the questions of the discontinuity of the extreme oscillation exponents on the set of linear homogeneous differential systems with continuous coefficients on the positive axis. The existence of points on a set of differential systems is established in which all the higher and lower exponents of the oscillation zeros, roots, and hypercorns are not only not continuous, but are not continuous either from above or from below. Moreover, the non-invariance of the extreme exponent of oscillations with respect to infinitesimal perturbations has been proved. When proving the results of this work, the cases of parity and odd order of the matrix of the system are considered separately.","PeriodicalId":41162,"journal":{"name":"Advances in Differential Equations and Control Processes","volume":"10 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78762919","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
Secular Terms for the Kinetic Mckean Model 动力学Mckean模型的长期术语
IF 0.1
Advances in Differential Equations and Control Processes Pub Date : 2023-01-01 DOI: 10.21638/11701/spbu35.2023.108
S. Dukhnovsky
{"title":"Secular Terms for the Kinetic Mckean Model","authors":"S. Dukhnovsky","doi":"10.21638/11701/spbu35.2023.108","DOIUrl":"https://doi.org/10.21638/11701/spbu35.2023.108","url":null,"abstract":"In this article, we investigate the kinetic McKean model. The perturbed solution of the Cauchy problem is sought in the form of Fourier series. The Fourier coefficients for the zero and nonzero modes are written out, respectively. The original system is reduced to an infinite system of differential equations. An approximation for the systems is constructed. Under certain assumptions, we find secular terms (non-integrable part). This, in turn, will allow us to prove for the first time the exponential stabilization of the solution in the future.","PeriodicalId":41162,"journal":{"name":"Advances in Differential Equations and Control Processes","volume":"47 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82225027","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 Existence and Uniqueness of a Positive Solution to a Boundary Value Problem for One Nonlinear Functional - Differential Equation of Even Order 一类偶阶非线性泛函微分方程边值问题正解的存在唯一性
IF 0.1
Advances in Differential Equations and Control Processes Pub Date : 2023-01-01 DOI: 10.21638/11701/spbu35.2023.103
{"title":"On the Existence and Uniqueness of a Positive Solution to a Boundary Value Problem for One Nonlinear Functional - Differential Equation of Even Order","authors":"","doi":"10.21638/11701/spbu35.2023.103","DOIUrl":"https://doi.org/10.21638/11701/spbu35.2023.103","url":null,"abstract":"In this article, we consider a two-point boundary value problem for one nonlinear functional differential equation of even order with strong non-linearity on segment [0,1] with homogeneous boundary conditions. With the use of special topological means, sufficient conditions for the existence and uniqueness of a positive solution to the problem under consideration. Existence of a positive solution proved using the well-known Krasnoselsky theorem on a fixed point in a cone, uniqueness is respectively established using the contraction mapping principle. A non-trivial example is given, illustrating the fulfillment of sufficient conditions unique solvability of the problem.","PeriodicalId":41162,"journal":{"name":"Advances in Differential Equations and Control Processes","volume":"130 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79361157","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 One Problem of Controlling an Airplane-type Unmanned Aerial Vehicle with Given Intermediate Values of Different Parts of Coordinates 给定不同坐标部分中间值的飞机型无人机控制问题
IF 0.1
Advances in Differential Equations and Control Processes Pub Date : 2023-01-01 DOI: 10.21638/11701/spbu35.2023.205
Vanya Rafaelovich Barseghyan, A. G. Matevosyan
{"title":"On One Problem of Controlling an Airplane-type Unmanned Aerial Vehicle with Given Intermediate Values of Different Parts of Coordinates","authors":"Vanya Rafaelovich Barseghyan, A. G. Matevosyan","doi":"10.21638/11701/spbu35.2023.205","DOIUrl":"https://doi.org/10.21638/11701/spbu35.2023.205","url":null,"abstract":"The mathematical model of spatial flight of an unmanned airplane-type vehicle is considered. For a linearized mathematical model of an unmanned aerial vehicle the problem of synthesis of control laws with given initial, finite values of the phase vector and intermediate values of different parts of coordinates at different moments of time is solved. A necessary and sufficient condition for the existence of program control and the corresponding motion is formulated. The control functions and corresponding phase trajectories of motion are constructed. As an application of the proposed approach, explicit expressions of the program control function and program motion are constructed for specific numerical values.","PeriodicalId":41162,"journal":{"name":"Advances in Differential Equations and Control Processes","volume":"54 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77623779","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 Boundedness of Solutions of a Quasilinear System of Ordinary Differential Equations 一类拟线性常微分方程组解的有界性
IF 0.1
Advances in Differential Equations and Control Processes Pub Date : 2023-01-01 DOI: 10.21638/11701/spbu35.2023.203
E. Mukhamadiev, A. Naimov
{"title":"On the Boundedness of Solutions of a Quasilinear System of Ordinary Differential Equations","authors":"E. Mukhamadiev, A. Naimov","doi":"10.21638/11701/spbu35.2023.203","DOIUrl":"https://doi.org/10.21638/11701/spbu35.2023.203","url":null,"abstract":"In the paper, the question of the boundedness of an arbitrary solution of a quasilinear system of ordinary differential equations is investigated under boundedness of the observed values of the solution. The observed values of the solution are a finite set of scalar products of the solution with given vectors. In terms of the properties of the matrix of coefficients of the system of equations and the matrix of coefficients of observed values, theorems on the boundedness of an arbitrary solution with boundedness of the observed values are formulated and proved. The novelty of this paper is that using the method of limit equations, estimates are derived from which the boundedness or stability follows an arbitrary solution of a quasilinear system in terms of boundedness or stability of the observed values of the solution.","PeriodicalId":41162,"journal":{"name":"Advances in Differential Equations and Control Processes","volume":"40 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86611291","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
A Regularized Asymptotic Solution of the Cauchy Problem for the Nonhomogeneous Schroedinger Equation in the Quasiclassical Approximation in the Presence of a "strong" Turning Point of the Limit Operator 在极限算子的“强”拐点存在下，非齐次薛定谔方程Cauchy问题的准经典近似正则渐近解
IF 0.1
Advances in Differential Equations and Control Processes Pub Date : 2023-01-01 DOI: 10.21638/11701/spbu35.2023.107
A. Eliseev, P. V. Kirichenko
{"title":"A Regularized Asymptotic Solution of the Cauchy Problem for the Nonhomogeneous Schroedinger Equation in the Quasiclassical Approximation in the Presence of a \"strong\" Turning Point of the Limit Operator","authors":"A. Eliseev, P. V. Kirichenko","doi":"10.21638/11701/spbu35.2023.107","DOIUrl":"https://doi.org/10.21638/11701/spbu35.2023.107","url":null,"abstract":"The article is devoted to the development of the regularization method by S.A. Lomov on singularly perturbed problems in the presence of spectral singularities of the limit operator. In particular, a regularized asymptotic solution is constructed for the singularly perturbed inhomogeneous Cauchy problem that arises in the quasiclassical approximation in the Schroedinger equation in the coordinate representation. The potential energy profile chosen in the paper leads to a singularity in the spectrum of the limit operator in the form of a <> turning point. Based on the ideas of asymptotic integration of problems with unstable spectrum, S.A. Lomov and A.G. Eliseev, it is indicated how and from what considerations regularizing functions and additional regularizing operators should be introduced, the formalism of the regularization method for the indicated type of singularity is described in detail, this algorithm is substantiated, and an asymptotic solution of any order with respect to a small parameter is constructed.","PeriodicalId":41162,"journal":{"name":"Advances in Differential Equations and Control Processes","volume":"10 1","pages":""},"PeriodicalIF":0.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88651547","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
OPTICAL SOLITON SOLUTIONS FOR THE NONLINEAR THIRD-ORDER PARTIAL DIFFERENTIAL EQUATION 非线性三阶偏微分方程的光孤子解
IF 0.1
Advances in Differential Equations and Control Processes Pub Date : 2022-12-22 DOI: 10.17654/0974324322037
S. Ibrahim
{"title":"OPTICAL SOLITON SOLUTIONS FOR THE NONLINEAR THIRD-ORDER PARTIAL DIFFERENTIAL EQUATION","authors":"S. Ibrahim","doi":"10.17654/0974324322037","DOIUrl":"https://doi.org/10.17654/0974324322037","url":null,"abstract":"","PeriodicalId":41162,"journal":{"name":"Advances in Differential Equations and Control Processes","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47909637","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: 2
SOLITARY WAVE SOLUTIONS FOR THE (2+1) CBS EQUATION (2+1) CBS方程的孤波解
IF 0.1
Advances in Differential Equations and Control Processes Pub Date : 2022-12-21 DOI: 10.17654/0974324322036
S. Ibrahim
{"title":"SOLITARY WAVE SOLUTIONS FOR THE (2+1) CBS EQUATION","authors":"S. Ibrahim","doi":"10.17654/0974324322036","DOIUrl":"https://doi.org/10.17654/0974324322036","url":null,"abstract":"","PeriodicalId":41162,"journal":{"name":"Advances in Differential Equations and Control Processes","volume":" ","pages":""},"PeriodicalIF":0.1,"publicationDate":"2022-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43775195","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: 2
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