发布求助
文献互助 智能选刊 最新文献

Differential Equations最新文献

筛选
英文 中文
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":"3 1","pages":""},"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":"5 1","pages":""},"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
System without Characteristic Directions with a Nonanalytic Center Condition 具有非解析中心条件的无特征方向系统
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-12-01 DOI: 10.1134/s0012266123120030
{"title":"System without Characteristic Directions with a Nonanalytic Center Condition","authors":"","doi":"10.1134/s0012266123120030","DOIUrl":"https://doi.org/10.1134/s0012266123120030","url":null,"abstract":"<span> <h3>Abstract</h3> <p> A real autonomous differential system of the fifth degree with a degenerate singular point without characteristic directions is obtained. The necessary and sufficient condition for the center at a given point is determined by a function that is not analytic at the boundary point of the set of system parameters for which the singular point of the system is monodromic. An asymptotic representation of this function is calculated at the point where its analyticity is violated. </p> </span>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"25 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139979106","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 Asymptotics of the Spectrum of an Integral Operator with a Logarithmic Kernel of a Special Form 论具有特殊形式对数核的积分算子谱的渐近性
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-12-01 DOI: 10.1134/s0012266123120121
{"title":"On Asymptotics of the Spectrum of an Integral Operator with a Logarithmic Kernel of a Special Form","authors":"","doi":"10.1134/s0012266123120121","DOIUrl":"https://doi.org/10.1134/s0012266123120121","url":null,"abstract":"<span> <h3>Abstract</h3> <p> We study the asymptotic behavior of the spectrum of an integral operator similar to an integral operator with a logarithmic kernel depending on the sum of arguments. By a simple change of variables, the corresponding equation is reduced to an integral equation of convolution type defined on a finite interval (as is well known, such equations in the general case cannot be solved by quadratures). Next, using the Fourier transform, the equation is reduced to a conjugation problem for analytic functions and then to an infinite system of linear algebraic equations, the isolation of the main terms in which allows deriving a relation that determines the spectrum of the original problem. </p> </span>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"29 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139979452","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 Properties of the Root Vector Function Systems of a $$2m $$ th-Order Dirac Type Operator with an Integrable Potential 具有可积势的$$2m $$ th阶Dirac型算子的根向量函数系的性质
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-11-23 DOI: 10.1134/s00122661230100014
E. C. Ibadov
{"title":"On the Properties of the Root Vector Function Systems of a $$2m $$ th-Order Dirac Type Operator with an Integrable Potential","authors":"E. C. Ibadov","doi":"10.1134/s00122661230100014","DOIUrl":"https://doi.org/10.1134/s00122661230100014","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a Dirac type operator with matrix coefficients. Estimates for the root vector\u0000functions are established, and criteria for the Bessel property and the unconditional basis property\u0000of the root vector function systems of this operator in the space <span>(L_{2}^{2m}(G) )</span>, where <span>(G=(a,b)subset mathbb {R} )</span> is a finite interval, are obtained.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"189 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538403","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
Some Theoretical Aspects of the Neural Network Approach to Stabilization of Switched Interval Systems 切换区间系统神经网络镇定的若干理论问题
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-11-23 DOI: 10.1134/s00122661230100099
A. S. Fursov, Yu. M. Mosolova
{"title":"Some Theoretical Aspects of the Neural Network Approach to Stabilization of Switched Interval Systems","authors":"A. S. Fursov, Yu. M. Mosolova","doi":"10.1134/s00122661230100099","DOIUrl":"https://doi.org/10.1134/s00122661230100099","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider the problem of stabilization of a switched interval linear system with slow\u0000switchings that are inaccessible to observation. It is proposed to look for a solution in the class of\u0000variable structure controllers. To ensure the functionality of such a controller, it is necessary to\u0000construct an observer of the switching signal. This paper is devoted to some theoretical issues\u0000related to the period of quantization of the neural observer’s operating time.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"22 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538413","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 a Control Problem for a System of Implicit Differential Equations 一类隐式微分方程组的控制问题
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-11-23 DOI: 10.1134/s0012266123090124
E. S. Zhukovskiy, I. D. Serova
{"title":"On a Control Problem for a System of Implicit Differential Equations","authors":"E. S. Zhukovskiy, I. D. Serova","doi":"10.1134/s0012266123090124","DOIUrl":"https://doi.org/10.1134/s0012266123090124","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider the differential inclusion <span>(F(t,x,dot {x})ni 0 )</span> with the constraint <span>(dot {x}(t)in B(t) )</span>, <span>(tin [a, b])</span>, on the\u0000derivative of the unknown function, where <span>(F)</span> and\u0000<span>(B )</span> are set-valued mappings, <span>(F:[a,b]times mathbb {R}^ntimes mathbb {R}^ntimes mathbb {R }^mrightrightarrows mathbb {R}^k )</span> is superpositionally measurable, and\u0000<span>( B:[a,b]rightrightarrows mathbb {R}^n)</span> is\u0000measurable. In terms of the properties of ordered covering and the monotonicity of set-valued\u0000mappings acting in finite-dimensional spaces, for the Cauchy problem we obtain conditions for the\u0000existence and estimates of solutions as well as conditions for the existence of a solution with the\u0000smallest derivative. Based on these results, we study a control system of the form\u0000<span>(f(t,x,dot {x},u)=0)</span>, <span>(dot {x}(t)in B(t) )</span>, <span>(u(t)in U(t,x,dot {x}) )</span>, <span>(tin [a,b])</span>.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"29 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538417","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
Existence of Two Solutions of the Inverse Problem for a Mathematical Model of Sorption Dynamics 一类吸附动力学数学模型反问题的两个解的存在性
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-11-23 DOI: 10.1134/s00122661230100105
A. M. Denisov, Zhu Dongqin
{"title":"Existence of Two Solutions of the Inverse Problem for a Mathematical Model of Sorption Dynamics","authors":"A. M. Denisov, Zhu Dongqin","doi":"10.1134/s00122661230100105","DOIUrl":"https://doi.org/10.1134/s00122661230100105","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The inverse problem for a nonlinear mathematical model of sorption dynamics with an\u0000unknown variable kinetic coefficient is considered. A theorem on the existence of two solutions of\u0000the inverse problem is proved, and an iterative method for solving it is justified. An example of\u0000the application of the proposed method to the numerical solution of the inverse problem is given.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"26 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538418","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
Regularity of the Pressure Function for Weak Solutions of the Nonstationary Navier–Stokes Equations 非平稳Navier-Stokes方程弱解压力函数的正则性
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-11-23 DOI: 10.1134/s0012266123090069
E. V. Amosova
{"title":"Regularity of the Pressure Function for Weak Solutions of the Nonstationary Navier–Stokes Equations","authors":"E. V. Amosova","doi":"10.1134/s0012266123090069","DOIUrl":"https://doi.org/10.1134/s0012266123090069","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the nonstationary system of Navier–Stokes equations for an incompressible fluid.\u0000Based on a regularized problem that takes into account the relaxation of the velocity field into a\u0000solenoidal field, the existence of a pressure function almost everywhere in the domain under\u0000consideration for solutions in the Hopf class is substantiated. Using the proposed regularization,\u0000we prove the existence of more regular weak solutions of the original problem without smallness\u0000restrictions on the original data. A uniqueness theorem is proven in the two-dimensional case.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"65 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538416","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
Cauchy Problem for the Nonlinear Liouville Equation in the Class of Periodic Infinite-Gap Functions 一类周期无限间隙函数中非线性Liouville方程的Cauchy问题
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-11-23 DOI: 10.1134/s00122661230100087
A. B. Khasanov, Kh. N. Normurodov, U. O. Khudayorov
{"title":"Cauchy Problem for the Nonlinear Liouville Equation in the Class of Periodic Infinite-Gap Functions","authors":"A. B. Khasanov, Kh. N. Normurodov, U. O. Khudayorov","doi":"10.1134/s00122661230100087","DOIUrl":"https://doi.org/10.1134/s00122661230100087","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> The inverse spectral problem method is used to integrate the nonlinear Liouville equation\u0000in the class of periodic infinite-gap functions. The evolution of the spectral data of the periodic\u0000Dirac operator whose coefficient is a solution of the nonlinear Liouville equation is introduced.\u0000The solvability of the Cauchy problem for an infinite system of Dubrovin differential equations in\u0000the class of three times continuously differentiable periodic infinite-gap functions is proved. It is\u0000shown that the sum of a uniformly convergent function series constructed by solving the Dubrovin\u0000system of equations and using the first trace formula satisfies the Liouville equation.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":"1 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538419","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
首页 上一页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信