首页 > 最新文献

Differential Equations最新文献

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 Q2 MATHEMATICS Pub Date : 2023-12-15 DOI: 10.1134/s00122661230130013
N. V. Zaitseva

Abstract

The paper considers nonlocal problems with integral conditions for hyperbolic equationswith the Bessel differential operator whose statement substantially depends on the intervals wherethe parameter occurring in this operator varies. The well-posedness of these problems is studiedaccording to a unified scheme based on the classical method of separation of variables, which isalso used to study nonclassical problems with integral conditions for equations ofelliptic–hyperbolic type containing the Bessel operator in one or two variables as well.

摘要 本文研究了带有贝塞尔微分算子的双曲方程的积分条件非局部问题,这些问题的表述在很大程度上取决于该算子中出现的参数变化的区间。根据基于经典变量分离法的统一方案,研究了这些问题的良好求解性,该方案也用于研究包含贝塞尔算子的单变量或双变量椭圆-双曲型方程的积分条件非经典问题。
{"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 Q2 MATHEMATICS Pub Date : 2023-12-01 DOI: 10.1134/s0012266123120054

Abstract

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.

摘要 本研究考虑了具有幂律非线性的椭圆方程和系统。分布式机器人编队建模以及化学动力学、生物学、天体物理学和许多其他领域都存在此类方程。研究了构建多维精确解的问题。建议使用一种特殊类型的解析,将问题简化为求解代数方程系统。通过明确的公式得到了一些新的多维精确解(包括径向对称和各向异性)的多参数族。举例说明了所发现的精确解。
{"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 Q2 MATHEMATICS Pub Date : 2023-12-01 DOI: 10.1134/s0012266123120030

Abstract

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.

摘要 获得了一个具有退化奇点且无特征方向的五阶实自微分系统。在系统奇点为单色性的系统参数集边界点上的非解析函数决定了在给定点上中心的必要和充分条件。在违反其解析性的点上计算该函数的渐近表示。
{"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 Q2 MATHEMATICS Pub Date : 2023-12-01 DOI: 10.1134/s0012266123120121

Abstract

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.

摘要 我们研究了一个积分算子频谱的渐近行为,该算子类似于一个具有对数核的积分算子,其对数核取决于参数之和。通过简单的变量变化,相应的方程被还原为定义在有限区间上的卷积型积分方程(众所周知,一般情况下此类方程无法通过二次方程求解)。接着,利用傅立叶变换,方程被简化为解析函数的共轭问题,然后又简化为一个无限线性代数方程组,通过分离其中的主要项,可以推导出确定原始问题频谱的关系。
{"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 Q2 MATHEMATICS Pub Date : 2023-11-23 DOI: 10.1134/s00122661230100014
E. C. Ibadov

Abstract

We consider a Dirac type operator with matrix coefficients. Estimates for the root vectorfunctions are established, and criteria for the Bessel property and the unconditional basis propertyof the root vector function systems of this operator in the space (L_{2}^{2m}(G) ), where (G=(a,b)subset mathbb {R} ) is a finite interval, are obtained.

考虑一类具有矩阵系数的Dirac型算子。建立了根向量函数的估计,得到了该算子的根向量函数系统在(G=(a,b)subset mathbb {R} )为有限区间的空间(L_{2}^{2m}(G) )上的贝塞尔性质和无条件基性质的判据。
{"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 Q2 MATHEMATICS Pub Date : 2023-11-23 DOI: 10.1134/s00122661230100099
A. S. Fursov, Yu. M. Mosolova

Abstract

We consider the problem of stabilization of a switched interval linear system with slowswitchings that are inaccessible to observation. It is proposed to look for a solution in the class ofvariable structure controllers. To ensure the functionality of such a controller, it is necessary toconstruct an observer of the switching signal. This paper is devoted to some theoretical issuesrelated to the period of quantization of the neural observer’s operating time.

考虑一类不可观测的切换区间线性系统的镇定问题。提出了在变结构控制器中寻找解的方法。为了保证这种控制器的功能,有必要构造一个开关信号的观测器。本文研究了神经观测器工作时间量化周期的一些理论问题。
{"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 Q2 MATHEMATICS Pub Date : 2023-11-23 DOI: 10.1134/s0012266123090124
E. S. Zhukovskiy, I. D. Serova

Abstract

We consider the differential inclusion (F(t,x,dot {x})ni 0 ) with the constraint (dot {x}(t)in B(t) ), (tin [a, b]), on thederivative of the unknown function, where (F) and(B ) are set-valued mappings, (F:[a,b]times mathbb {R}^ntimes mathbb {R}^ntimes mathbb {R }^mrightrightarrows mathbb {R}^k ) is superpositionally measurable, and( B:[a,b]rightrightarrows mathbb {R}^n) ismeasurable. In terms of the properties of ordered covering and the monotonicity of set-valuedmappings acting in finite-dimensional spaces, for the Cauchy problem we obtain conditions for theexistence and estimates of solutions as well as conditions for the existence of a solution with thesmallest derivative. Based on these results, we study a control system of the form(f(t,x,dot {x},u)=0), (dot {x}(t)in B(t) ), (u(t)in U(t,x,dot {x}) ), (tin [a,b]).

摘要考虑未知函数导数的微分包含(F(t,x,dot {x})ni 0 )和约束(dot {x}(t)in B(t) ), (tin [a, b]),其中(F)和(B )是集值映射,(F:[a,b]times mathbb {R}^ntimes mathbb {R}^ntimes mathbb {R }^mrightrightarrows mathbb {R}^k )是叠加可测的,( B:[a,b]rightrightarrows mathbb {R}^n)是可测的。利用有限维空间中集值映射的有序覆盖性质和单调性,得到了柯西问题解的存在性、估计性和导数最小解的存在性条件。基于这些结果,我们研究了一种形式为(f(t,x,dot {x},u)=0), (dot {x}(t)in B(t) ), (u(t)in U(t,x,dot {x}) ), (tin [a,b])的控制系统。
{"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 Q2 MATHEMATICS Pub Date : 2023-11-23 DOI: 10.1134/s00122661230100105
A. M. Denisov, Zhu Dongqin

Abstract

The inverse problem for a nonlinear mathematical model of sorption dynamics with anunknown variable kinetic coefficient is considered. A theorem on the existence of two solutions ofthe inverse problem is proved, and an iterative method for solving it is justified. An example ofthe application of the proposed method to the numerical solution of the inverse problem is given.

摘要考虑了具有未知变量动力学系数的非线性吸附动力学数学模型的反问题。证明了反问题存在两个解的定理,并证明了求解反问题的迭代方法。最后给出了该方法在反问题数值解中的应用实例。
{"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 Q2 MATHEMATICS Pub Date : 2023-11-23 DOI: 10.1134/s0012266123090069
E. V. Amosova

Abstract

We study the nonstationary system of Navier–Stokes equations for an incompressible fluid.Based on a regularized problem that takes into account the relaxation of the velocity field into asolenoidal field, the existence of a pressure function almost everywhere in the domain underconsideration for solutions in the Hopf class is substantiated. Using the proposed regularization,we prove the existence of more regular weak solutions of the original problem without smallnessrestrictions on the original data. A uniqueness theorem is proven in the two-dimensional case.

研究不可压缩流体的非定常Navier-Stokes方程组。基于一个考虑速度场弛豫为螺线场的正则化问题,证明了在Hopf类解的考虑域中几乎处处存在压力函数。利用提出的正则化方法,我们证明了原问题存在更正则的弱解,而不受原始数据的小约束。在二维情况下证明了唯一性定理。
{"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 Q2 MATHEMATICS Pub Date : 2023-11-23 DOI: 10.1134/s00122661230100087
A. B. Khasanov, Kh. N. Normurodov, U. O. Khudayorov

Abstract

The inverse spectral problem method is used to integrate the nonlinear Liouville equationin the class of periodic infinite-gap functions. The evolution of the spectral data of the periodicDirac operator whose coefficient is a solution of the nonlinear Liouville equation is introduced.The solvability of the Cauchy problem for an infinite system of Dubrovin differential equations inthe class of three times continuously differentiable periodic infinite-gap functions is proved. It isshown that the sum of a uniformly convergent function series constructed by solving the Dubrovinsystem of equations and using the first trace formula satisfies the Liouville equation.

摘要利用逆谱问题方法对一类周期无限间隙函数中的非线性Liouville方程进行积分。介绍了系数为非线性Liouville方程解的周期性dirac算子谱数据的演化过程。证明了一类三次连续可微周期无限间隙函数的无限Dubrovin微分方程组的Cauchy问题的可解性。通过求解杜布罗文方程组,利用第一迹公式构造的一致收敛函数级数的和满足Liouville方程。
{"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
期刊
Differential Equations
全部 Acc. Chem. Res. ACS Applied Bio Materials ACS Appl. Electron. Mater. ACS Appl. Energy Mater. ACS Appl. Mater. Interfaces ACS Appl. Nano Mater. ACS Appl. Polym. Mater. ACS BIOMATER-SCI ENG ACS Catal. ACS Cent. Sci. ACS Chem. Biol. ACS Chemical Health & Safety ACS Chem. Neurosci. ACS Comb. Sci. ACS Earth Space Chem. ACS Energy Lett. ACS Infect. Dis. ACS Macro Lett. ACS Mater. Lett. ACS Med. Chem. Lett. ACS Nano ACS Omega ACS Photonics ACS Sens. ACS Sustainable Chem. Eng. ACS Synth. Biol. Anal. Chem. BIOCHEMISTRY-US Bioconjugate Chem. BIOMACROMOLECULES Chem. Res. Toxicol. Chem. Rev. Chem. Mater. CRYST GROWTH DES ENERG FUEL Environ. Sci. Technol. Environ. Sci. Technol. Lett. Eur. J. Inorg. Chem. IND ENG CHEM RES Inorg. Chem. J. Agric. Food. Chem. J. Chem. Eng. Data J. Chem. Educ. J. Chem. Inf. Model. J. Chem. Theory Comput. J. Med. Chem. J. Nat. Prod. J PROTEOME RES J. Am. Chem. Soc. LANGMUIR MACROMOLECULES Mol. Pharmaceutics Nano Lett. Org. Lett. ORG PROCESS RES DEV ORGANOMETALLICS J. Org. Chem. J. Phys. Chem. J. Phys. Chem. A J. Phys. Chem. B J. Phys. Chem. C J. Phys. Chem. Lett. Analyst Anal. Methods Biomater. Sci. Catal. Sci. Technol. Chem. Commun. Chem. Soc. Rev. CHEM EDUC RES PRACT CRYSTENGCOMM Dalton Trans. Energy Environ. Sci. ENVIRON SCI-NANO ENVIRON SCI-PROC IMP ENVIRON SCI-WAT RES Faraday Discuss. Food Funct. Green Chem. Inorg. Chem. Front. Integr. Biol. J. Anal. At. Spectrom. J. Mater. Chem. A J. Mater. Chem. B J. Mater. Chem. C Lab Chip Mater. Chem. Front. Mater. Horiz. MEDCHEMCOMM Metallomics Mol. Biosyst. Mol. Syst. Des. Eng. Nanoscale Nanoscale Horiz. Nat. Prod. Rep. New J. Chem. Org. Biomol. Chem. Org. Chem. Front. PHOTOCH PHOTOBIO SCI PCCP Polym. Chem.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
×
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
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1