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Infinitely many solutions for Kirchhoff-type equations involving critical growth in Orlicz-Sobolev with negative energies 负能量Orlicz-Sobolev中涉及临界增长的kirchhoff型方程的无穷多解
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-06-24 DOI: 10.21136/AM.2025.0059-25
Elmostafa Bendib, Mustapha Khiddi
{"title":"Infinitely many solutions for Kirchhoff-type equations involving critical growth in Orlicz-Sobolev with negative energies","authors":"Elmostafa Bendib,&nbsp;Mustapha Khiddi","doi":"10.21136/AM.2025.0059-25","DOIUrl":"10.21136/AM.2025.0059-25","url":null,"abstract":"<div><p>We investigate a class of Kirchhoff-type equations characterized by critical growth within Orlicz-Sobolev spaces. The main result establishes the existence of infinitely many solutions with negative energy. Using an adapted concentration-compactness principle and advanced variational methods, we overcome key challenges such as non-compactness and non-differentiability to the associated functionals. This work extends existing results to more general functional spaces, offering new insights into nonlocal nonlinear equations.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 3","pages":"441 - 456"},"PeriodicalIF":0.7,"publicationDate":"2025-06-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169373","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
H∞ analysis of cooperative multi-agent systems by adaptive interpolation 基于自适应插值的协同多智能体系统H∞分析
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-06-17 DOI: 10.21136/AM.2025.0218-24
Zoran Tomljanović
{"title":"H∞ analysis of cooperative multi-agent systems by adaptive interpolation","authors":"Zoran Tomljanović","doi":"10.21136/AM.2025.0218-24","DOIUrl":"10.21136/AM.2025.0218-24","url":null,"abstract":"<div><p>We consider a projection-based model reduction approach to computing the maximal impact, one agent or a group of agents has on the cooperative system. As a criterion for measuring the agent-team impact on multi-agent systems, we use the <i>H</i><sub>∞</sub> norm, and output synchronization is taken as the underlying cooperative control scheme. We investigate a projection-based model reduction approach that allows efficient <i>H</i><sub>∞</sub> norm calculation. The convergence of this approach depends on initial interpolation points, so we present approaches to their determination. Since the analysis of multi-agent systems is important from different perspectives, several comparisons are presented in the section on numerical experiments. A graph Laplacian matrix of an inter-agent interaction graph is a foundational element in modeling and analyzing multi-agent systems. We consider various graph topology matrices, system parameters, and excitations of different agents. Different strategies for selecting initial interpolation points are also compared with baseline approaches for calculating the <i>H</i><sub>∞</sub> norm.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 3","pages":"367 - 386"},"PeriodicalIF":0.7,"publicationDate":"2025-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145166458","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
Discontinuous Galerkin method with Godunov-like numerical fluxes for traffic flows on networks. Part I: L2 stability 网络上交通流的类godunov数值流的不连续伽辽金方法。第一部分：L2稳定性
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-06-12 DOI: 10.21136/AM.2025.0017-25
Lukáš Vacek, Chi-Wang Shu, Václav Kučera
{"title":"Discontinuous Galerkin method with Godunov-like numerical fluxes for traffic flows on networks. Part I: L2 stability","authors":"Lukáš Vacek,&nbsp;Chi-Wang Shu,&nbsp;Václav Kučera","doi":"10.21136/AM.2025.0017-25","DOIUrl":"10.21136/AM.2025.0017-25","url":null,"abstract":"<div><p>We study the stability of a discontinuous Galerkin (DG) method applied to the numerical solution of traffic flow problems on networks. We discretize the Lighthill-Whitham-Richards equations on each road by DG. At traffic junctions, we consider two types of numerical fluxes that are based on Godunov’s numerical flux derived in a previous work of ours. These fluxes are easily constructible for any number of incoming and outgoing roads, respecting the drivers’ preferences. The analysis is split into two parts: in Part I, contained in this paper, we analyze the stability of the resulting numerical scheme in the <i>L</i><sup>2</sup>-norm. The resulting estimates allow for a linear-in-time growth of the square of the <i>L</i><sup>2</sup>-norm of the DG solution. This is observed in numerical experiments in certain situations with traffic congestions. Next, we prove that under certain assumptions on the junction parameters (number of incoming and outgoing roads and drivers’ preferences) the DG solution satisfies an entropy inequality where the square entropy is nonincreasing in time. Numerical experiments are presented. The work is complemented by the followup paper, Part II, where a maximum principle is proved for the DG scheme with limiters.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 3","pages":"311 - 339"},"PeriodicalIF":0.7,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164618","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
Discontinuous Galerkin method with Godunov-like numerical fluxes for traffic flows on networks. Part II: Maximum principle 网络上交通流的类godunov数值流的不连续伽辽金方法。第二部分：最大原则
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-06-12 DOI: 10.21136/AM.2025.0018-25
Lukáš Vacek, Chi-Wang Shu, Václav Kučera
{"title":"Discontinuous Galerkin method with Godunov-like numerical fluxes for traffic flows on networks. Part II: Maximum principle","authors":"Lukáš Vacek,&nbsp;Chi-Wang Shu,&nbsp;Václav Kučera","doi":"10.21136/AM.2025.0018-25","DOIUrl":"10.21136/AM.2025.0018-25","url":null,"abstract":"<div><p>We prove the maximum principle for a discontinuous Galerkin (DG) method applied to the numerical solution of traffic flow problems on networks described by the Lighthill-Whitham-Richards equations. The paper is a followup of the preceding paper, Part I, where <i>L</i><sup><i>2</i></sup> stability of the scheme is analyzed. At traffic junctions, we consider numerical fluxes based on Godunov’s flux derived in our previous work. We also construct a new Godunov-like numerical flux taking into account right of way at the junction to cover a wider variety of scenarios in the analysis. These fluxes are easily constructible for any number of incoming and outgoing roads, respecting the drivers’ preferences. We prove that the explicit Euler or SSP DG scheme with limiters satisfies a maximum principle on general networks. Numerical experiments demonstrate the obtained results.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 3","pages":"341 - 366"},"PeriodicalIF":0.7,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164619","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 regular time-periodic solutions for a class of non-Newtonian double-diffusive convection system 一类非牛顿双扩散对流系统正则时间周期解的存在性
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-06-09 DOI: 10.21136/AM.2025.0268-24
Qiong Wu, Changjia Wang
{"title":"Existence of regular time-periodic solutions for a class of non-Newtonian double-diffusive convection system","authors":"Qiong Wu,&nbsp;Changjia Wang","doi":"10.21136/AM.2025.0268-24","DOIUrl":"10.21136/AM.2025.0268-24","url":null,"abstract":"<div><p>We investigate a system of partial differential equations that models the motion of an incompressible double-diffusion convection fluid. The additional stress tensor is generated by a potential with <i>p</i>-structure. In a three-dimensional periodic setting and <span>(p in [{{5} over {3}},2))</span>, we employ a regularized approximation scheme in conjunction with the Galerkin method to establish the existence of regular solutions, provided that the forcing term is properly small. Furthermore, we demonstrate the existence of periodic regular solutions with period <i>T</i> when the external force exhibits periodicity in time with the same period <i>T</i>.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 3","pages":"387 - 411"},"PeriodicalIF":0.7,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163510","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
WENO-Z scheme with new nonlinear weights for Hamilton-Jacobi equations and adaptive approximation Hamilton-Jacobi方程新的非线性权值WENO-Z格式和自适应逼近
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-05-28 DOI: 10.21136/AM.2025.0258-24
Kwangil Kim, Kwanhung Ri, Wonho Han
{"title":"WENO-Z scheme with new nonlinear weights for Hamilton-Jacobi equations and adaptive approximation","authors":"Kwangil Kim,&nbsp;Kwanhung Ri,&nbsp;Wonho Han","doi":"10.21136/AM.2025.0258-24","DOIUrl":"10.21136/AM.2025.0258-24","url":null,"abstract":"<div><p>A new fifth-order weighted essentially nonoscillatory (WENO) scheme is designed to approximate Hamilton-Jacobi equations. As employing a fifth-order linear approximation and three third-order ones on the same six-point stencil as before, a newly considered WENO-Z methodology is adapted to define nonlinear weights and the final WENO reconstruction results in a simple and clear convex combination. The scheme has formal fifth-order accuracy in smooth regions of the solution and nonoscillating behavior nearby singularities. A full account is given of the key role of parameters in WENO reconstruction and their selection. The latter half describes the adaptive stage on WENO approximation in convergence framework, which enables us to get the numerical solution to converge still achieving high-order accuracy for the nonconvex problems where the pure WENO scheme fails to converge. Detailed numerical experiments are performed to demonstrate the ability of the proposed numerical methods.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 3","pages":"413 - 439"},"PeriodicalIF":0.7,"publicationDate":"2025-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170476","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
Exponential stability for Timoshenko model with thermal effect 热效应下Timoshenko模型的指数稳定性
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-05-13 DOI: 10.21136/AM.2025.0161-24
Luiz Gutemberg Rosário Miranda, Bruno Magalhães Alves
{"title":"Exponential stability for Timoshenko model with thermal effect","authors":"Luiz Gutemberg Rosário Miranda,&nbsp;Bruno Magalhães Alves","doi":"10.21136/AM.2025.0161-24","DOIUrl":"10.21136/AM.2025.0161-24","url":null,"abstract":"<div><p>We performe an exponential decay analysis for a Timoshenko-type system under the thermal effect by constructing the Lyapunov functional. More precisely, this thermal effect is acting as a mechanism for dissipating energy generated by the bending of the beam, acting only on the vertical displacement equation, different from other works already existing in the literature. Furthermore, we show the good placement of the problem using semigroup theory.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 2","pages":"149 - 168"},"PeriodicalIF":0.7,"publicationDate":"2025-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145165279","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 nontrivial solutions for modified fractional Schrödinger-Poisson systems via perturbation method 用摄动法研究修正分数阶Schrödinger-Poisson系统非平凡解的存在性
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-05-12 DOI: 10.21136/AM.2025.0232-23
Atefe Goli, Sayyed Hashem Rasouli, Somayeh Khademloo
{"title":"On the existence of nontrivial solutions for modified fractional Schrödinger-Poisson systems via perturbation method","authors":"Atefe Goli,&nbsp;Sayyed Hashem Rasouli,&nbsp;Somayeh Khademloo","doi":"10.21136/AM.2025.0232-23","DOIUrl":"10.21136/AM.2025.0232-23","url":null,"abstract":"<div><p>The existence of nontrivial solutions is considered for the fractional Schrödinger-Poisson system with double quasi-linear terms: </p><div><div><span>$$begin{cases}(-Delta)^{s}u+V(x)u+phi u -{1over2}u (-Delta)^{s}u^{2}=f(x,u), &amp; xinmathbb{R}^{3} , (-Delta)^{t} phi= u^{2}, &amp; xinmathbb{R}^{3},end{cases}$$</span></div></div><p> where (−Δ)<sup><i>α</i></sup> is the fractional Laplacian for <i>α</i> = <i>s</i>, <i>t</i> ∈ (0, 1] with <i>s</i> &lt; <i>t</i> and 2<i>t</i> + 4<i>s</i> &gt; 3. Under assumptions on <i>V</i> and <i>f</i>, we prove the existence of positive solutions and negative solutions for the above system by using perturbation method and the mountain pass theorem.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 2","pages":"293 - 310"},"PeriodicalIF":0.7,"publicationDate":"2025-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145164229","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
Local accuracy in finite element analysis using curved isoparametric elements 曲面等参单元有限元分析中的局部精度
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-05-07 DOI: 10.21136/AM.2025.0049-25
Pranjal Saxena, Chandra Shekhar Upadhyay
{"title":"Local accuracy in finite element analysis using curved isoparametric elements","authors":"Pranjal Saxena,&nbsp;Chandra Shekhar Upadhyay","doi":"10.21136/AM.2025.0049-25","DOIUrl":"10.21136/AM.2025.0049-25","url":null,"abstract":"<div><p>The finite element method (FEM) is popularly used for numerically approximating PDE(s) over complicated domains due to its rich mathematical background, versatility, and ease of implementation. In this article, we investigate one of its important features, i.e., the approximation of PDE(s) over nonpolygonal Lipschitz domains by higher-order simplicial elements in 2D and 3D. This important issue is not well understood and often ignored by engineers due to its mathematical complexity, i.e., the FEM approximation of curved domains results in inexact boundary conditions, which is a variational crime. This article explores the role of approximation at curved boundaries. Further, the effect of incompleteness of the approximation space also contributes to the error induced in the curved elements. A simple benchmark test for errors is proposed. Tests are conducted for subparametric and isoparametric approximations. Comparison with isogeometric analysis (IGA) is also presented to highlight the basic differences and advantages of isoparametric elements.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 2","pages":"257 - 292"},"PeriodicalIF":0.7,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145163242","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
Capacity solutions for a degenerate pi(x)-Laplacian thermistor system with electrical conductivities 具有电导率的退化pi(x)-拉普拉斯热敏电阻系统的容量解
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 2025-04-04 DOI: 10.21136/AM.2025.0220-24
Hichem Khelifi
{"title":"Capacity solutions for a degenerate pi(x)-Laplacian thermistor system with electrical conductivities","authors":"Hichem Khelifi","doi":"10.21136/AM.2025.0220-24","DOIUrl":"10.21136/AM.2025.0220-24","url":null,"abstract":"<div><p>We establish the existence of a capacity solution for a degenerate anisotropic stationary system with variable exponents and electrical conductivity. The system is a generalization of the thermistor problem, addressing the interaction between temperature and electric potential within semiconductor material.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"70 2","pages":"203 - 230"},"PeriodicalIF":0.7,"publicationDate":"2025-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161654","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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