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Differential Equations最新文献

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On a Positional Control Problem for a Nonlinear Equation with Distributed Parameters 关于具有分布参数的非线性方程的位置控制问题
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-12-29 DOI: 10.1134/s00122661230110071
V. I. Maksimov
{"title":"On a Positional Control Problem for a Nonlinear Equation with Distributed Parameters","authors":"V. I. Maksimov","doi":"10.1134/s00122661230110071","DOIUrl":"https://doi.org/10.1134/s00122661230110071","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a guaranteed control problem for a nonlinear distributed equation of diffusion\u0000type. The problem is essentially to construct a feedback control algorithm ensuring that the\u0000solution of a given equation tracks the solution of a similar equation subjected to an unknown\u0000disturbance. The case in which a discontinuous unbounded function can be a feasible disturbance\u0000is studied. We solve the problem under conditions of inaccurate measurement of solutions of each\u0000of the equations at discrete instants of time and indicate a solution algorithm robust under\u0000information noise and calculation errors.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139072371","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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 Construction of the Graph of Discrete States of a Switched Affine System 论构建开关仿射系统的离散状态图
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-12-29 DOI: 10.1134/s00122661230110095
A. S. Fursov, P. A. Krylov
{"title":"On the Construction of the Graph of Discrete States of a Switched Affine System","authors":"A. S. Fursov, P. A. Krylov","doi":"10.1134/s00122661230110095","DOIUrl":"https://doi.org/10.1134/s00122661230110095","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The problem of constructing the graph of states of a switched affine system closed by a\u0000static state feedback is considered. To solve this problem, a constructive algorithm based on the\u0000study of the consistency of systems of linear algebraic inequalities is proposed.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066391","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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 Relationship Between the Pontryagin Maximum Principle and the Hamilton–Jacobi–Bellman Equation in Optimal Control Problems for Fractional-Order Systems 论分数阶系统优化控制问题中庞特里亚金最大原则与汉密尔顿-雅各比-贝尔曼方程之间的关系
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-12-29 DOI: 10.1134/s0012266123011006x
M. I. Gomoyunov
{"title":"On the Relationship Between the Pontryagin Maximum Principle and the Hamilton–Jacobi–Bellman Equation in Optimal Control Problems for Fractional-Order Systems","authors":"M. I. Gomoyunov","doi":"10.1134/s0012266123011006x","DOIUrl":"https://doi.org/10.1134/s0012266123011006x","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider the optimal control problem of minimizing the terminal cost functional for a\u0000dynamical system whose motion is described by a differential equation with Caputo fractional\u0000derivative. The relationship between the necessary optimality condition in the form of\u0000Pontryagin’s maximum principle and the Hamilton–Jacobi–Bellman equation with so-called\u0000fractional coinvariant derivatives is studied. It is proved that the costate variable in the\u0000Pontryagin maximum principle coincides, up to sign, with the fractional coinvariant gradient of\u0000the optimal result functional calculated along the optimal motion.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066404","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hopf Bifurcation in a Predator–Prey System with Infection 有感染的捕食者-猎物系统中的霍普夫分岔
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-12-29 DOI: 10.1134/s00122661230110125
A. P. Krishchenko, O. A. Podderegin
{"title":"Hopf Bifurcation in a Predator–Prey System with Infection","authors":"A. P. Krishchenko, O. A. Podderegin","doi":"10.1134/s00122661230110125","DOIUrl":"https://doi.org/10.1134/s00122661230110125","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study a model of a predator–prey system with possible infection of prey in the form of\u0000a three-dimensional system of ordinary differential equations. Using the localization method of\u0000compact invariant sets, the existence of an attractor is proved and a compact positively invariant\u0000set is found that estimates its position. The conditions for the extinction of populations and the\u0000existence of equilibria are found. A numerical method for finding a Hopf bifurcation of the inner\u0000equilibrium is proposed and an example of an arising stable limit cycle is given.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Nonlinear Boundary Value Problems for Differential Inclusions 论微分夹杂的非线性边界问题
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-12-29 DOI: 10.1134/s00122661230110010
A. V. Arutyunov, Z. T. Zhukovskaya, S. E. Zhukovskiy
{"title":"On Nonlinear Boundary Value Problems for Differential Inclusions","authors":"A. V. Arutyunov, Z. T. Zhukovskaya, S. E. Zhukovskiy","doi":"10.1134/s00122661230110010","DOIUrl":"https://doi.org/10.1134/s00122661230110010","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider autonomous differential inclusions with nonlinear boundary conditions.\u0000Sufficient conditions for the existence of solutions in the class of absolutely continuous functions\u0000are obtained for these inclusions. It is shown that the corresponding existence theorem applies to\u0000the Cauchy problem and the antiperiodic boundary value problem. The result is used to derive a\u0000new mean value inequality for continuously differentiable functions.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Solvability of Linear Differential Equations 线性微分方程的可解性
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-12-29 DOI: 10.1134/s00122661230110034
V. S. Mokeichev, A. M. Sidorov
{"title":"Solvability of Linear Differential Equations","authors":"V. S. Mokeichev, A. M. Sidorov","doi":"10.1134/s00122661230110034","DOIUrl":"https://doi.org/10.1134/s00122661230110034","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We propose a new approach to the solvability of ordinary as well as partial differential\u0000equations in the theory of linear differential equations and also in the theory of integral equations.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Bounded Real Lemma for the Anisotropic Norm of Time-invariant Systems with Multiplicative Noises 具有乘法噪声的时不变系统的各向异性规范的有界实数定理
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-12-29 DOI: 10.1134/s00122661230110101
A. V. Yurchenkov, I. R. Belov
{"title":"Bounded Real Lemma for the Anisotropic Norm of Time-invariant Systems with Multiplicative Noises","authors":"A. V. Yurchenkov, I. R. Belov","doi":"10.1134/s00122661230110101","DOIUrl":"https://doi.org/10.1134/s00122661230110101","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a discrete-time-invariant system with multiplicative noise with\u0000implementation in the state space. The exogenous disturbance is chosen from the class of\u0000time-invariant ergodic sequences of nonzero colorness. We consider the level of mean anisotropy of\u0000the exogenous disturbance to be bounded by a known value. Conditions for the anisotropic norm\u0000to be bounded by a given number are obtained in terms of solving a matrix system of inequalities\u0000with a convex constraint of a special type. It is demonstrated how, on the basis of the obtained\u0000conditions, to construct a static state control that ensures the minimum value of the anisotropic\u0000norm of the system enclosed by this control.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Behavior of Trajectories of a Four-Dimensional Model of HIV Infection 艾滋病毒感染四维模型的轨迹行为
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-12-29 DOI: 10.1134/s00122661230110022
A. N. Kanatnikov, O. S. Tkacheva
{"title":"Behavior of Trajectories of a Four-Dimensional Model of HIV Infection","authors":"A. N. Kanatnikov, O. S. Tkacheva","doi":"10.1134/s00122661230110022","DOIUrl":"https://doi.org/10.1134/s00122661230110022","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A model of interaction between the human immunodeficiency virus and the human\u0000immune system is considered. Equilibria in the state space of the system and their stability are\u0000analyzed, and the ultimate bounds of the trajectories are constructed. It has been proved that the\u0000local asymptotic stability of the equilibrium corresponding to the absence of disease is equivalent\u0000to its global asymptotic stability. The loss of stability is shown to be caused by a transcritical\u0000bifurcation.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139066389","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mixed Problems with Integral Conditions for Hyperbolic Equations with the Bessel Operator 带积分条件的贝塞尔算子双曲方程混合问题
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-12-15 DOI: 10.1134/s00122661230130013
N. V. Zaitseva
{"title":"Mixed Problems with Integral Conditions for Hyperbolic Equations with the Bessel Operator","authors":"N. V. Zaitseva","doi":"10.1134/s00122661230130013","DOIUrl":"https://doi.org/10.1134/s00122661230130013","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The paper considers nonlocal problems with integral conditions for hyperbolic equations\u0000with the Bessel differential operator whose statement substantially depends on the intervals where\u0000the parameter occurring in this operator varies. The well-posedness of these problems is studied\u0000according to a unified scheme based on the classical method of separation of variables, which is\u0000also used to study nonclassical problems with integral conditions for equations of\u0000elliptic–hyperbolic type containing the Bessel operator in one or two variables as well.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138692327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Exact Solutions of a Multidimensional System of Elliptic Equations with Power-Law Nonlinearities 论带有幂律非线性的多维椭圆方程系统的精确解
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-12-01 DOI: 10.1134/s0012266123120054
{"title":"On Exact Solutions of a Multidimensional System of Elliptic Equations with Power-Law Nonlinearities","authors":"","doi":"10.1134/s0012266123120054","DOIUrl":"https://doi.org/10.1134/s0012266123120054","url":null,"abstract":"<span> <h3>Abstract</h3> <p> Equations and systems of elliptic type with power-law nonlinearities are considered. Such equations are found in modeling distributed robotic formations, as well as in chemical kinetics, biology, astrophysics, and many other fields. The problem of constructing multidimensional exact solutions is studied. It is proposed to use a special type of ansatz that reduces the problem to solving systems of algebraic equations. A number of multiparameter families of new exact multidimensional solutions (both radially symmetric and anisotropic) represented by explicit formulas are obtained. Examples are given to illustrate the exact solutions found. </p> </span>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139979120","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","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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