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Acta Applicandae Mathematicae最新文献

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A Numerical Study on Singularity Formation of the 2D Ideal MHD Equations 二维理想MHD方程奇点形成的数值研究
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2025-01-29 DOI: 10.1007/s10440-025-00710-4
Daisuke Hirata
{"title":"A Numerical Study on Singularity Formation of the 2D Ideal MHD Equations","authors":"Daisuke Hirata","doi":"10.1007/s10440-025-00710-4","DOIUrl":"10.1007/s10440-025-00710-4","url":null,"abstract":"<div><p>In this note, we study numerically the regularity issue of the ideal MHD equations on the two-dimensional torus. By pseudo-spectral method, we provide evidence that a certain numerical solution is initially regular and eventually very singular in finite time.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"195 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143110181","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
Multiplicity of Solutions for a Kirchhoff Multi-Phase Problem with Variable Exponents 一类变指数Kirchhoff多相问题解的多重性
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2025-01-24 DOI: 10.1007/s10440-025-00711-3
Francesca Vetro
{"title":"Multiplicity of Solutions for a Kirchhoff Multi-Phase Problem with Variable Exponents","authors":"Francesca Vetro","doi":"10.1007/s10440-025-00711-3","DOIUrl":"10.1007/s10440-025-00711-3","url":null,"abstract":"<div><p>In this paper, we study a Kirchhoff-type problem driven by a multi-phase operator with three variable exponents. Such problem has a right-hand side consisting of a Carathéodory perturbation which is defined only locally as well as the Kirchhoff term. Using a generalized version of the symmetric mountain pass theorem along with recent a priori upper bounds for multi-phase problems, we get whole a sequence of nontrivial solutions for our problem converging to zero in the appropriate Musielak-Orlicz Sobolev space and in <span>(L^{infty }(Omega ))</span>.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"195 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143109312","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
Asymptotic Expansion of Solutions of the 2nd Order Difference Equations in an Unbounded Domain 无界域上二阶差分方程解的渐近展开
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2025-01-15 DOI: 10.1007/s10440-025-00706-0
Sofia V. Rumyantseva
{"title":"Asymptotic Expansion of Solutions of the 2nd Order Difference Equations in an Unbounded Domain","authors":"Sofia V. Rumyantseva","doi":"10.1007/s10440-025-00706-0","DOIUrl":"10.1007/s10440-025-00706-0","url":null,"abstract":"<div><p>Difference equations play a crucial role in a wide array of mathematical and physical tasks. In this article, we focus on the analysis of a second order linear homogeneous difference equation with smooth coefficients via WKB method. It is well-known that such equations exhibit two WKB solutions in a segment devoid of turning and singular points. We establish a theorem demonstrating the existence of these solutions in an unbounded domain under certain conditions regarding the smoothness and growth behavior of the coefficients at infinity. Furthermore, using this theorem, we derive the asymptotic expansion of Laguerre polynomials for large orders and values, yielding estimates that align with existing results.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"195 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142976442","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 of Highly Nonlinear Hybrid Neutral Pantograph Stochastic Systems with Multiple Delays 多时滞高非线性混合中性受电弓随机系统的指数稳定性
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2025-01-14 DOI: 10.1007/s10440-025-00705-1
Abdellatif Ben Makhlouf, Aws Ben Hamed, Lassaad Mchiri, Mohamed Rhaima
{"title":"Exponential Stability of Highly Nonlinear Hybrid Neutral Pantograph Stochastic Systems with Multiple Delays","authors":"Abdellatif Ben Makhlouf,&nbsp;Aws Ben Hamed,&nbsp;Lassaad Mchiri,&nbsp;Mohamed Rhaima","doi":"10.1007/s10440-025-00705-1","DOIUrl":"10.1007/s10440-025-00705-1","url":null,"abstract":"<div><p>This paper addresses the existence and exponential stability problem of highly nonlinear hybrid neutral pantograph stochastic equations with multiple delays (HNPSDEswMD). By Lyapunov functional method and without laying down a linear growth condition, the above problem of the exact solution is shown. We end up with two numerical examples that corroborates our theoretical findings.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"195 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142976409","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
Continuous Dependence Result for a Class of Evolutionary Variational-Hemivariational Inequalities with Application to a Dynamic Thermo-Viscoelastic Contact Problem 一类演化变分-半变分不等式的连续相关结果及其在动态热粘弹性接触问题中的应用
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2025-01-13 DOI: 10.1007/s10440-025-00707-z
Abdelhafid Ouaanabi, Mohammed Alaoui, Mustapha Bouallala, El Hassan Essoufi
{"title":"Continuous Dependence Result for a Class of Evolutionary Variational-Hemivariational Inequalities with Application to a Dynamic Thermo-Viscoelastic Contact Problem","authors":"Abdelhafid Ouaanabi,&nbsp;Mohammed Alaoui,&nbsp;Mustapha Bouallala,&nbsp;El Hassan Essoufi","doi":"10.1007/s10440-025-00707-z","DOIUrl":"10.1007/s10440-025-00707-z","url":null,"abstract":"<div><p>In the present paper, we consider a mathematical model describing the dynamic Coulomb’s frictional contact between a thermo-viscoelastic body and a thermally conductive rigid foundation. We employ the nonlinear constitutive viscoelastic law with long-term memory and thermal effects. We describe some contact and thermal conditions with the Clarke subdifferential boundary conditions. We derive the weak formulation of the problem as a system coupling two variational-hemivariational inequalities. We provide results on the existence and uniqueness of a weak solution to the model by using recent results from the theory of variational-hemivariational inequalities. Finally, the continuous dependence of the solution on the data is derived by applying an abstract result that we demonstrate.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"195 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142976565","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
Memory Based Approaches to One-Dimensional Nonlinear Models 基于记忆的一维非线性模型方法
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-12-16 DOI: 10.1007/s10440-024-00703-9
Amir Naseem, Ioannis K. Argyros, Sania Qureshi, Muhammad Aziz ur Rehman, Amanullah Soomro, Krzysztof Gdawiec, Ridwanulahi Iyanda Abdulganiy
{"title":"Memory Based Approaches to One-Dimensional Nonlinear Models","authors":"Amir Naseem,&nbsp;Ioannis K. Argyros,&nbsp;Sania Qureshi,&nbsp;Muhammad Aziz ur Rehman,&nbsp;Amanullah Soomro,&nbsp;Krzysztof Gdawiec,&nbsp;Ridwanulahi Iyanda Abdulganiy","doi":"10.1007/s10440-024-00703-9","DOIUrl":"10.1007/s10440-024-00703-9","url":null,"abstract":"<div><p>Algorithms that locate roots are used to analyze nonlinear equations in computer science, mathematics, and physical sciences. In order to speed up convergence and increase computational efficiency, memory-based root-seeking algorithms may look for the previous iterations. Three memory-based methods with a convergence order of about 2.4142 and one method without memory with third-order convergence are devised using both Taylor’s expansion and the backward difference operator. We provide an extensive analysis of local and semilocal convergence. We also use polynomiography to analyze the methods visually. Finally, the proposed iterative approaches outperform a number of existing memory-based methods when applied to one-dimensional nonlinear models taken from different fields of science and engineering.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"195 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142826093","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
Preservation of Relative Hazard Rate and Relative Reversed Hazard Rate Orders by Distorted Distributions 通过扭曲分布保留相对危险率和相对反向危险率阶次
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-12-13 DOI: 10.1007/s10440-024-00704-8
Mohamed Kayid, Raghad A. Almohsen
{"title":"Preservation of Relative Hazard Rate and Relative Reversed Hazard Rate Orders by Distorted Distributions","authors":"Mohamed Kayid,&nbsp;Raghad A. Almohsen","doi":"10.1007/s10440-024-00704-8","DOIUrl":"10.1007/s10440-024-00704-8","url":null,"abstract":"<div><p>In this paper, we establish preservation properties of relative aging orders under distorted distributions. The relative hazard rate order and the relative reversed hazard rate order are considered. Using the derived results, a preservation property of the relative hazard rate order and a preservation property of the relative reversed hazard rate order derived perviously by Misra and Francis (Stat. Probab. Lett. 106:272–280, 2015) for, respectively, parallel and series systems are strengthened. Examples are also presented to illustrate the applicability of the obtained results.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"194 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142821483","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
Influence of Gauges in the Numerical Simulation of the Time-Dependent Ginzburg-Landau Model 量规在时变金兹堡-朗道模型数值模拟中的影响
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-11-15 DOI: 10.1007/s10440-024-00701-x
Cyril Tain, Jean-Guy Caputo, Ionut Danaila
{"title":"Influence of Gauges in the Numerical Simulation of the Time-Dependent Ginzburg-Landau Model","authors":"Cyril Tain,&nbsp;Jean-Guy Caputo,&nbsp;Ionut Danaila","doi":"10.1007/s10440-024-00701-x","DOIUrl":"10.1007/s10440-024-00701-x","url":null,"abstract":"<div><p>The time-dependent Ginzburg-Landau (TDGL) model requires the choice of a gauge for the problem to be mathematically well-posed. In the literature, three gauges are commonly used: the Coulomb gauge, the Lorenz gauge and the temporal gauge. It has been noticed (J. Fleckinger-Pellé et al. in Dynamics of the Ginzburg-Landau equations of superconductivity, Technical report, Argonne National Lab. (ANL), Argonne, IL, United States, 1997) that these gauges can be continuously related by a single parameter considering the more general <span>(omega )</span>-gauge, where <span>(omega )</span> is a non-negative real parameter. In this article, we study the influence of the gauge parameter <span>(omega )</span> on the convergence of numerical simulations of the TDGL model using finite element schemes. A classical benchmark is first analysed for different values of <span>(omega )</span> and artefacts are observed for lower values of <span>(omega )</span>. Then, we relate these observations with a systematic study of convergence orders in the unified <span>(omega )</span>-gauge framework. In particular, we show the existence of a tipping point value for <span>(omega )</span>, separating optimal convergence behaviour and a degenerate one. We find that numerical artefacts are correlated to the degeneracy of the convergence order of the method and we suggest strategies to avoid such undesirable effects. New 3D configurations are also investigated (the sphere with or without geometrical defect).</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"194 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142645417","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 Properties on the Reversibility and the Linear Response Theory of Langevin Dynamics 朗文动力学的可逆性和线性响应理论的一些特性
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-11-14 DOI: 10.1007/s10440-024-00702-w
Yuan Gao, Jian-Guo Liu, Zibu Liu
{"title":"Some Properties on the Reversibility and the Linear Response Theory of Langevin Dynamics","authors":"Yuan Gao,&nbsp;Jian-Guo Liu,&nbsp;Zibu Liu","doi":"10.1007/s10440-024-00702-w","DOIUrl":"10.1007/s10440-024-00702-w","url":null,"abstract":"<div><p>Linear response theory is a fundamental framework studying the macroscopic response of a physical system to an external perturbation. This paper focuses on the rigorous mathematical justification of linear response theory for Langevin dynamics. We give some equivalent characterizations for reversible overdamped/underdamped Langevin dynamics, which is the unperturbed reference system. Then we clarify sufficient conditions for the smoothness and exponential convergence to the invariant measure for the overdamped case. We also clarify those sufficient conditions for the underdamped case, which corresponds to hypoellipticity and hypocoercivity. Based on these, the asymptotic dependence of the response function on the small perturbation is proved in both finite and infinite time horizons. As applications, Green-Kubo relations and linear response theory for a generalized Langevin dynamics are also proved in a rigorous fashion.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"194 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636905","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
Reduced Order Model Based Nonlinear Waveform Inversion for the 1D Helmholtz Equation 基于减阶模型的一维赫尔姆霍兹方程非线性波形反演
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-11-13 DOI: 10.1007/s10440-024-00700-y
Andreas Tataris, Tristan van Leeuwen
{"title":"Reduced Order Model Based Nonlinear Waveform Inversion for the 1D Helmholtz Equation","authors":"Andreas Tataris,&nbsp;Tristan van Leeuwen","doi":"10.1007/s10440-024-00700-y","DOIUrl":"10.1007/s10440-024-00700-y","url":null,"abstract":"<div><p>We study a reduced order model (ROM) based waveform inversion method applied to a Helmholtz problem with impedance boundary conditions and variable refractive index. The first goal of this paper is to obtain relations that allow the reconstruction of the Galerkin projection of the continuous problem onto the space spanned by solutions of the Helmholtz equation. The second goal is to study the introduced nonlinear optimization method based on the ROM aimed to estimate the refractive index from reflection and transmission data. Finally we compare numerically our method to the conventional least squares inversion based on minimizing the distance between modelled to measured data.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"194 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142636919","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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