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
Initial Value Problem for a Third-Order Nonlinear Integro-Differential Equation of Convolution Type 卷积型三阶非线性积分微分方程的初值问题
IF 0.6 4区 数学
Differential Equations Pub Date : 2024-07-30 DOI: 10.1134/s0012266124040086
S. N. Askhabov
{"title":"Initial Value Problem for a Third-Order Nonlinear Integro-Differential Equation of Convolution Type","authors":"S. N. Askhabov","doi":"10.1134/s0012266124040086","DOIUrl":"https://doi.org/10.1134/s0012266124040086","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> In this paper, we obtain two-sided a priori estimates for the solution of a homogeneous\u0000third-order Volterra integro-differential equation with a power-law nonlinearity and difference\u0000kernel. It is shown that the lower a priori estimate, which plays the role of a weight function when\u0000constructing a metric in the cone of the space of continuous functions, is sharp. Using these\u0000estimates, by the weighted metric method (an analog of A. Bielecki’s method), we prove a global\u0000theorem on the existence and uniqueness of a nontrivial solution of the initial value problem for\u0000this integro-differential equation in the class of nonnegative continuous functions on the positive\u0000half-line and on the method for finding this solution. It is shown that the solution can be found by\u0000the successive approximation method, and an estimate of the rate of convergence of the\u0000approximations to the exact solution is obtained. Examples are given to illustrate the results\u0000obtained.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867279","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 Eighty-Fifth Anniversary of Viktor Antonovich Sadovnichii 纪念维克托-安东诺维奇-萨多夫尼奇诞辰八十五周年
IF 0.6 4区 数学
Differential Equations Pub Date : 2024-07-30 DOI: 10.1134/s0012266124040013
{"title":"On the Eighty-Fifth Anniversary of Viktor Antonovich Sadovnichii","authors":"","doi":"10.1134/s0012266124040013","DOIUrl":"https://doi.org/10.1134/s0012266124040013","url":null,"abstract":"","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867341","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 Realization of Finite Essential Spectra of Oscillation Exponents of Two-Dimensional Differential Systems 论二维微分系统振荡指数有限本质谱的实现
IF 0.6 4区 数学
Differential Equations Pub Date : 2024-07-30 DOI: 10.1134/s0012266124040062
A. Kh. Stash, N. A. Loboda
{"title":"On the Realization of Finite Essential Spectra of Oscillation Exponents of Two-Dimensional Differential Systems","authors":"A. Kh. Stash, N. A. Loboda","doi":"10.1134/s0012266124040062","DOIUrl":"https://doi.org/10.1134/s0012266124040062","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> For any finite set of nonnegative numbers containing zero, we construct a two-dimensional\u0000linear homogeneous differential system (periodic if all elements of the given set are pairwise\u0000commensurate) in which the spectra of the oscillation exponents of signs, zeros, roots, and\u0000hyperroots coincide with this set, and all the values of these exponents are essential.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867281","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
Singularly Perturbed Optimal Tracking Problem 奇异扰动优化跟踪问题
IF 0.6 4区 数学
Differential Equations Pub Date : 2024-07-30 DOI: 10.1134/s0012266124040116
V. A. Sobolev
{"title":"Singularly Perturbed Optimal Tracking Problem","authors":"V. A. Sobolev","doi":"10.1134/s0012266124040116","DOIUrl":"https://doi.org/10.1134/s0012266124040116","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We consider a singularly perturbed optimal tracking problem with a given reference path\u0000in the case of incomplete information about the state vector in the presence of exogenous\u0000disturbances. To analyze the differential equations that arise when solving this problem, we use\u0000the decomposition method, which is based on the technique of integral manifolds of fast and slow\u0000motions.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873003","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
Christoffel–Darboux Formula for Polynomial Eigenfunctions of Second-Order Linear Differential Equations 二阶线性微分方程多项式特征函数的 Christoffel-Darboux 公式
IF 0.6 4区 数学
Differential Equations Pub Date : 2024-07-30 DOI: 10.1134/s0012266124040037
V. E. Kruglov
{"title":"Christoffel–Darboux Formula for Polynomial Eigenfunctions of Second-Order Linear Differential Equations","authors":"V. E. Kruglov","doi":"10.1134/s0012266124040037","DOIUrl":"https://doi.org/10.1134/s0012266124040037","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> Using recurrence relations between any three consecutive polynomial eigenfunctions of\u0000second-order linear differential equations, the Christoffel–Darboux formulas are derived for the\u0000system of polynomial eigenfunctions of these equations.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867276","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
Stabilization of a Switched System with Commensurate Delays under Slow Switchings 慢速切换下具有相应延迟的切换系统的稳定问题
IF 0.6 4区 数学
Differential Equations Pub Date : 2024-07-30 DOI: 10.1134/s0012266124040104
A. V. Il’in, A. S. Fursov
{"title":"Stabilization of a Switched System with Commensurate Delays under Slow Switchings","authors":"A. V. Il’in, A. S. Fursov","doi":"10.1134/s0012266124040104","DOIUrl":"https://doi.org/10.1134/s0012266124040104","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> An approach is proposed to constructing a digital controller that stabilizes a\u0000continuous-time switched linear system with commensurate delays in control under slow\u0000switchings. The approach to stabilization consistently includes the construction of a switched\u0000continuous–discrete-time closed-loop system with a digital controller, the transition to its\u0000discrete-time model, represented in the form of a switched system with modes of different orders,\u0000simultaneous stabilization of the subsystems of the resulting discrete-time model, and calculation\u0000of a delay time that ensures the stability of the original switched system closed by the controller\u0000found.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873062","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
Asymptotically Stable Solutions with Boundary and Internal Layers in Direct and Inverse Problems for a Singularly Perturbed Heat Equation with Nonlinear Thermal Diffusion 具有非线性热扩散的奇异扰动热方程的直接问题和逆问题中带有边界层和内部层的渐近稳定解
IF 0.6 4区 数学
Differential Equations Pub Date : 2024-07-30 DOI: 10.1134/s0012266124040025
M. A. Davydova, G. D. Rublev
{"title":"Asymptotically Stable Solutions with Boundary and Internal Layers in Direct and Inverse Problems for a Singularly Perturbed Heat Equation with Nonlinear Thermal Diffusion","authors":"M. A. Davydova, G. D. Rublev","doi":"10.1134/s0012266124040025","DOIUrl":"https://doi.org/10.1134/s0012266124040025","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> This paper proposes a new approach to the study of direct and inverse problems for a\u0000singularly perturbed heat equation with nonlinear temperature-dependent diffusion, based on the\u0000further development and use of asymptotic analysis methods in the nonlinear singularly perturbed\u0000reaction–diffusion–advection problems. The essence of the approach is presented using the\u0000example of one class of one-dimensional stationary problems with nonlinear boundary conditions,\u0000for which the case of applicability of asymptotic analysis is singled out. Sufficient conditions for\u0000the existence of classical solutions of the boundary layer type and the type of contrast structures\u0000are formulated, asymptotic approximations of an arbitrary order of accuracy to such solutions are\u0000constructed, algorithms for constructing formal asymptotics are substantiated, and the Lyapunov\u0000asymptotic stability of stationary solutions with boundary and internal layers as solutions of the\u0000corresponding parabolic problems is investigated. A class of nonlinear problems that take into\u0000account lateral heat exchange with the environment according to Newton’s law is considered.\u0000A theorem on the existence and uniqueness of a classical solution with boundary layers in\u0000problems of this type is proved. As applications of this research, methods for solving specific\u0000direct and inverse problems of nonlinear heat transfer related to increasing the operating efficiency\u0000of rectilinear heating elements in the smelting furnaces (heat exchangers) are presented, which\u0000include the calculation of thermal fields in the heating elements and a method for reconstructing\u0000thermal diffusion and heat transfer coefficients based on modeling data.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867342","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
An Inverse Problem for the Wave Equation with Two Nonlinear Terms 带有两个非线性项的波方程反问题
IF 0.6 4区 数学
Differential Equations Pub Date : 2024-07-30 DOI: 10.1134/s0012266124040074
V. G. Romanov
{"title":"An Inverse Problem for the Wave Equation with Two Nonlinear Terms","authors":"V. G. Romanov","doi":"10.1134/s0012266124040074","DOIUrl":"https://doi.org/10.1134/s0012266124040074","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> An inverse problem for a second-order hyperbolic equation containing two nonlinear terms\u0000is studied. The problem is to reconstruct the coefficients of the nonlinearities. The Cauchy\u0000problem with a point source located at a point <span>(mathbf {y})</span> is\u0000considered. This point is a parameter of the problem and successively runs over a spherical surface\u0000<span>(S )</span>. It is assumed that the desired coefficients are\u0000nonzero only in a domain lying inside <span>(S)</span>. The trace of the\u0000solution of the Cauchy problem on <span>(S)</span> is specified for all\u0000possible values of <span>( mathbf {y})</span> and for times close to the arrival of\u0000the wave from the source to the points on the surface <span>(S )</span>; this allows reducing the inverse problem under\u0000consideration to two successively solved problems of integral geometry. Solution stability estimates\u0000are found for these two problems.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873002","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 Existence of Nonlinearizable Solutions of a Nonclassical Two-Parameter Nonlinear Boundary Value Problem 论非经典双参数非线性边界问题的可非线性化解的存在性
IF 0.6 4区 数学
Differential Equations Pub Date : 2024-07-30 DOI: 10.1134/s0012266124040049
V. Yu. Martynova
{"title":"On the Existence of Nonlinearizable Solutions of a Nonclassical Two-Parameter Nonlinear Boundary Value Problem","authors":"V. Yu. Martynova","doi":"10.1134/s0012266124040049","DOIUrl":"https://doi.org/10.1134/s0012266124040049","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> A nonlinear eigenvalue problem for a system of three equations with boundary conditions\u0000of the first kind, describing the propagation of electromagnetic waves in a plane nonlinear\u0000waveguide, is considered. This is a two-parameter problem with one spectral parameter and a\u0000second parameter arising from an additional condition. This condition connects the integration\u0000constants that arise when finding the first integrals of the system. The existence of nonlinearizable\u0000solutions of the problem is proved.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867277","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
Optimization Inverse Spectral Problem for the One-Dimensional Schrödinger Operator on the Entire Real Line 全实线上一维薛定谔算子的优化反谱问题
IF 0.6 4区 数学
Differential Equations Pub Date : 2024-07-30 DOI: 10.1134/s0012266124040050
V. A. Sadovnichii, Ya. T. Sultanaev, N. F. Valeev
{"title":"Optimization Inverse Spectral Problem for the One-Dimensional Schrödinger Operator on the Entire Real Line","authors":"V. A. Sadovnichii, Ya. T. Sultanaev, N. F. Valeev","doi":"10.1134/s0012266124040050","DOIUrl":"https://doi.org/10.1134/s0012266124040050","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> We study the statement of the optimization inverse spectral problem with incomplete\u0000spectral data for the one-dimensional Schrödinger operator on the entire axis: for a given\u0000potential <span>(q_0 )</span>, find the closest function <span>(hat {q} )</span> such that the first <span>(m )</span> eigenvalues of the Schrödinger operator\u0000with potential <span>(hat {q})</span> coincide with given values <span>(lambda _k^*in mathbb {R} )</span>, <span>(k={1,dots ,m})</span>.\u0000</p>","PeriodicalId":50580,"journal":{"name":"Differential Equations","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141867278","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 下一页 尾页
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