Mathematical Methods in the Applied Sciences最新文献

{"title":"Estimates for the Diameters of the Set of Solutions to a Nonlinear Differential Equation With Unbounded Coefficients","authors":"Kordan Ospanov,&nbsp;Myrzagali Ospanov","doi":"10.1002/mma.10658","DOIUrl":"https://doi.org/10.1002/mma.10658","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we prove some estimates of the distribution functions of the Kolmogorov diameters of solution's set to one class of the third-order nonlinear differential equations with variable coefficients. The equation is defined on the entire real axis, and its coefficients are unbounded functions. Previously, such equations were studied in the case where their intermediate coefficients are equal to zero, and the junior coefficient does not change sign. Sufficient conditions for the existence of a weak solution are also obtained, and under some restrictions on the oscillation of the intermediate coefficient, the maximal regularity of the solution is proved in the paper. In the proofs of the theorems are use the results of the authors obtained in the case of a linear differential equation of the third order (Ospanov &amp; Ospanov, 2024), and Schauder's fixed point theorem.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"6103-6109"},"PeriodicalIF":2.1,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143594850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exact Boundary Controllability for a System of Coupled Wave Equations in Noncylindrical Domains","authors":"Ruikson. S. O. Nunes","doi":"10.1002/mma.10706","DOIUrl":"https://doi.org/10.1002/mma.10706","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper concerns to study an exact boundary controllability problem for a system of \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation>$$ m $$</annotation>\u0000 </semantics></math> coupled wave equations in domains with moving boundaries. Such systems model the vibrations of \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 </mrow>\u0000 <annotation>$$ m $$</annotation>\u0000 </semantics></math> identical flexible bodies coupled in parallel by means of an elastic layer where their boundaries present a bounded movement. The control is square integrable and acts on all moving boundary, and it is obtained by means of conormal derivative of the solution. The controllability method used here is that one established by D. L. Russell.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6671-6677"},"PeriodicalIF":2.1,"publicationDate":"2025-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On a Truncated Thermoelastic Timoshenko System With a Dual-Phase Lag Model","authors":"Salim A. Messaoudi,&nbsp;Ahmed Keddi,&nbsp;Mohamed Alahyane","doi":"10.1002/mma.10708","DOIUrl":"https://doi.org/10.1002/mma.10708","url":null,"abstract":"<div>\u0000 \u0000 <p>In this work, we consider a one-dimensional truncated Timoshenko system coupled with a heat equation, where the heat flux is given by the generalized dual-phase lag model. By using the semigroup theory and some nonclassical differential operators, we establish the well-posedness of the problem. Then, we use the multiplier method to show that the only one heat control is enough to stabilize the whole system exponentially without imposing the usual equal-speed assumption or any other stability number. Moreover, to illustrate our theoretical results, we give some numerical tests. Our result seems to be the first of this type.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6691-6703"},"PeriodicalIF":2.1,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622386","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fractional Integration and Differentiation of Asymptotic Relations and Applications","authors":"Pavel Řehák","doi":"10.1002/mma.10679","DOIUrl":"https://doi.org/10.1002/mma.10679","url":null,"abstract":"<div>\u0000 \u0000 <p>The main results of this paper show how asymptotic relations are preserved when integrated or differentiated in the sense of fractional operators. In some of them, the concept of regular variation plays a role. We derive a fractional extension of the Karamata integration theorem and of the monotone density theorem, among others. We offer several approaches that provide deeper insight into relationships between different concepts. Illustrative applications in fractional differential equations are also presented.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6381-6395"},"PeriodicalIF":2.1,"publicationDate":"2025-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Novel Algorithm and Its Convergence Analysis for Solving the Generalized Split Inverse Problem","authors":"Mohammad Eslamian","doi":"10.1002/mma.10639","DOIUrl":"https://doi.org/10.1002/mma.10639","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we consider a bilevel problem: Variational inequalities over the solution set of a general split inverse problem consists of a monotone variational inclusion problem. We propose a relaxed inertial forward-backward-forward splitting algorithm with a new step size rule for finding an approximate solution of this problem in real Hilbert spaces. Under some mild conditions, we prove a strong convergence theorem for the algorithm produced by the method. Also, we apply our result to study certain classes of bilevel optimization problems, and split inverse problems. Finally, we present some numerical experiments and application in signal recovery problem to demonstrate the efficiency of the proposed algorithm.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5822-5837"},"PeriodicalIF":2.1,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Numerical Solution of Second-Order Impulsive Differential Equations With Loadings Subject to Integral Boundary Conditions","authors":"Zhazira Kadirbayeva,&nbsp;Roza Kadirbayeva","doi":"10.1002/mma.10670","DOIUrl":"https://doi.org/10.1002/mma.10670","url":null,"abstract":"<div>\u0000 \u0000 <p>In this paper, we present a computational method for solving the second-order impulsive differential equations with loadings subject to integral boundary conditions based on the Dzhumabaev parametrization method. The idea of this method involves introducing additional parameters, reducing the original problem to solving a system of linear algebraic equations. The system's coefficients and right-hand side are determined by solving Cauchy problems for ODEs and by calculating definite integrals. Four examples are provided to show the effectiveness and feasibility of the main results.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6269-6277"},"PeriodicalIF":2.1,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Constrained Minimizers of the Fourth-Order Schrödinger Equation With Saturable Nonlinearity","authors":"Zeye Han","doi":"10.1002/mma.10685","DOIUrl":"https://doi.org/10.1002/mma.10685","url":null,"abstract":"&lt;div&gt;\u0000 \u0000 &lt;p&gt;In this paper, we consider the existence of normalized solutions for the following fourth-order Schrödinger equation with saturated nonlinearity: \u0000&lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mfenced&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mtable&gt;\u0000 &lt;mtr&gt;\u0000 &lt;mtd&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Δ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;Δ&lt;/mi&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;I&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;I&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;mi&gt;u&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 ","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6488-6494"},"PeriodicalIF":2.1,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622636","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Stability of Discontinuous Galerkin Methods for Volterra Integral Equations","authors":"Jiao Wen,&nbsp;Min Li,&nbsp;Hongbo Guan","doi":"10.1002/mma.10649","DOIUrl":"https://doi.org/10.1002/mma.10649","url":null,"abstract":"<div>\u0000 \u0000 <p>We conduct the stability analysis of discontinuous Galerkin methods applied to Volterra integral equations in this paper. Stability conditions with respect to both the basic and convolution test equations are derived. Our findings indicate that the methods with orders up to 6 exhibit \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>A</mi>\u0000 </mrow>\u0000 <annotation>$$ A $$</annotation>\u0000 </semantics></math>-stability when applied with the basic test equation, while demonstrating unbounded stability regions when applied to the convolution test equation. Additionally, the results of \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>V</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 </msub>\u0000 </mrow>\u0000 <annotation>$$ {V}_0 $$</annotation>\u0000 </semantics></math>-stability for the semidiscretized variants (quadrature discontinuous Galerkin methods) and fully discretized versions (fully discretized discontinuous Galerkin methods) with orders 1 and 2 are presented when solving the convolution test equation. To corroborate these theoretical results, we provide some numerical experiments for validation.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 5","pages":"5972-5986"},"PeriodicalIF":2.1,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143595085","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Optimization of Robin Laplacian Eigenvalue With Indefinite Weight in Spherical Shell","authors":"Baruch Schneider,&nbsp;Diana Schneiderová,&nbsp;Yifan Zhang","doi":"10.1002/mma.10697","DOIUrl":"https://doi.org/10.1002/mma.10697","url":null,"abstract":"<div>\u0000 \u0000 <p>This paper is concerned with an optimization problem of Robin Laplacian eigenvalue with respect to an indefinite weight, which is formulated as a shape optimization problem thanks to the known bang–bang distribution of the optimal weight function. The minimization of the principal eigenvalue of the problem in a spherical shell of an arbitrary dimension is fully solved.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6586-6591"},"PeriodicalIF":2.1,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Decay of Solutions of Nonhomogenous Hyperbolic Equations","authors":"Piotr Michał Bies","doi":"10.1002/mma.10678","DOIUrl":"https://doi.org/10.1002/mma.10678","url":null,"abstract":"<div>\u0000 \u0000 <p>We consider conditions for the decay in time of solutions of nonhomogenous hyperbolic equations. It is proven that solutions of the equations go to 0 in \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>L</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow>\u0000 <annotation>$$ {L}&amp;#x0005E;2 $$</annotation>\u0000 </semantics></math> at infinity if and only if an equation's right-hand side uniquely determines the initial conditions in a certain way. We also obtain that a hyperbolic equation has a unique solution that vanishes when \u0000<span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>t</mi>\u0000 <mo>→</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$$ tto infty $$</annotation>\u0000 </semantics></math>.</p>\u0000 </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6375-6380"},"PeriodicalIF":2.1,"publicationDate":"2025-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143622608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}