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Differential Equations最新文献

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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":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":"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":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":"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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":null,"pages":null},"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
Gellerstedt Problem with a Nonlocal Oddness Boundary Condition for the Lavrent’ev–Bitsadze Equation Lavrent 'ev-Bitsadze方程非局部奇异边界条件下的Gellerstedt问题
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-11-23 DOI: 10.1134/s00122661230100051
T. E. Moiseev
{"title":"Gellerstedt Problem with a Nonlocal Oddness Boundary Condition for the Lavrent’ev–Bitsadze Equation","authors":"T. E. Moiseev","doi":"10.1134/s00122661230100051","DOIUrl":"https://doi.org/10.1134/s00122661230100051","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the Gellerstedt problem for the Lavrent’ev–Bitsadze equation with the oddness\u0000boundary condition on the boundary of the ellipticity domain. All eigenvalues and eigenfunctions\u0000are obtained in closed form. It is proved that the system of eigenfunctions is complete in the\u0000elliptic part of the domain and incomplete in the entire domain. The unique solvability of the\u0000problem is also proved; the solution is written in the form of a series if the spectral parameter is\u0000not equal to an eigenvalue. For the spectral parameter coinciding with an eigenvalue, solvability\u0000conditions are obtained under which the family of solutions is found in the form of a series. A\u0000condition for the solvability of the problem depending on the eigenvalues is obtained. The\u0000constructed analytical solutions can be used efficiently in numerical modeling of transonic gas\u0000dynamics problems.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538410","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
Approximation to the Sturm–Liouville Problem with a Discontinuous Nonlinearity 具有不连续非线性的Sturm-Liouville问题的逼近
IF 0.6 4区 数学
Differential Equations Pub Date : 2023-11-23 DOI: 10.1134/s0012266123090045
D. K. Potapov
{"title":"Approximation to the Sturm–Liouville Problem with a Discontinuous Nonlinearity","authors":"D. K. Potapov","doi":"10.1134/s0012266123090045","DOIUrl":"https://doi.org/10.1134/s0012266123090045","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a continuous approximation to the Sturm–Liouville problem with\u0000a nonlinearity discontinuous in the phase variable. The approximating problem is obtained from\u0000the original one by small perturbations of the spectral parameter and by approximating the\u0000nonlinearity by Carathéodory functions. The variational method is used to prove the\u0000theorem on the proximity of solutions of the approximating and original problems. The resulting\u0000theorem is applied to the one-dimensional Gol’dshtik and Lavrent’ev models of separated flows.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2023-11-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138538412","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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