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Structural Similarity in Joint Inverse Problems 关节反问题的结构相似性
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2025-10-03 DOI: 10.1007/s10440-025-00748-4
Teun Schilperoort, Tristan van Leeuwen
{"title":"Structural Similarity in Joint Inverse Problems","authors":"Teun Schilperoort,&nbsp;Tristan van Leeuwen","doi":"10.1007/s10440-025-00748-4","DOIUrl":"10.1007/s10440-025-00748-4","url":null,"abstract":"<div><p>Joint inverse problems occur in many practical situations, where different modalities are used to image the same object. Structural similarity is a way to regularize such joint inverse problems by imposing similarity between the images. While structural similarity has found widespread use in many practical settings, its theoretical foundations remain underexplored. This study develops an over-arching formulation for these types of problems and studies their well-posedness via the Direct Method from the calculus of variations. We focus in particular on lower semi-continuity and coerciveness as essential properties for the well-posedness of the variational problem in <span>(W^{m,p})</span> and <span>(SBV)</span>. Here quasiconvexity and growth properties of the structural similarity quantifier turns out to be essential. We find that the use of gradient-difference, cross-gradient or Schatten norms as structural similarity quantifiers is theoretically justified. A generalized form of the cross-gradient that inherently works on <span>(N)</span> coupled problems is introduced.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"199 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-025-00748-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145210867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Comparison Principles and Asymptotic Behavior of Delayed Age-Structured Neuron Models 延迟年龄结构神经元模型的比较原理和渐近行为
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2025-09-26 DOI: 10.1007/s10440-025-00746-6
María J. Cáceres, José A. Cañizo, Nicolas Torres
{"title":"Comparison Principles and Asymptotic Behavior of Delayed Age-Structured Neuron Models","authors":"María J. Cáceres,&nbsp;José A. Cañizo,&nbsp;Nicolas Torres","doi":"10.1007/s10440-025-00746-6","DOIUrl":"10.1007/s10440-025-00746-6","url":null,"abstract":"<div><p>In the context of neuroscience the elapsed-time model is an age-structured equation that describes the behavior of interconnected spiking neurons through the time since the last discharge, with many interesting dynamics depending on the type of interactions between neurons. We investigate the asymptotic behavior of this equation in the case of both discrete and distributed delays that account for the time needed to transmit a nerve impulse from one neuron to the rest of the ensemble. To prove the convergence to the equilibrium, we follow an approach based on comparison principles for Volterra equations involving the total activity, which provides a simpler and more straightforward alternative technique than those in the existing literature on the elapsed-time model.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"199 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169617","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
Recovering the Diffusion Coefficient in the Porous Medium Equation from a Large-Time Measurement 从大时间测量中恢复多孔介质方程中的扩散系数
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2025-09-25 DOI: 10.1007/s10440-025-00747-5
Hagop Karakazian, Toni Sayah, Faouzi Triki
{"title":"Recovering the Diffusion Coefficient in the Porous Medium Equation from a Large-Time Measurement","authors":"Hagop Karakazian,&nbsp;Toni Sayah,&nbsp;Faouzi Triki","doi":"10.1007/s10440-025-00747-5","DOIUrl":"10.1007/s10440-025-00747-5","url":null,"abstract":"<div><p>This paper addresses the time-dependent Porous Medium Equation, <span>(u_{t} - alpha Delta u^{gamma }= 0)</span> with polytropic exponent <span>(gamma &gt;1)</span> and diffusion coefficient <span>(alpha &gt;0)</span>. Given the value of <span>(gamma )</span> and the solution <span>(u)</span> at a large time <span>(T)</span>, our goal is to determine the parameter <span>(alpha )</span> without the knowledge of the initial data <span>(u(0))</span>. Leveraging an asymptotic inequality satisfied by <span>(u(T))</span>, we propose a numerical algorithm to recover <span>(alpha )</span> through a minimization problem. Furthermore, we establish an upper bound on the error between the exact and recovered values of <span>(alpha )</span> and perform numerical simulations in two and three dimensional cases.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"199 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168866","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
A Final Value Problem for the Nonlinear Modified Helmholtz Equation Associated with the Nonlinear Wave Velocity 与非线性波速相关的非线性修正Helmholtz方程的终值问题
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2025-09-23 DOI: 10.1007/s10440-025-00745-7
Long Pham Nguyen Hoang, Triet Le Minh, Phong Luu Hong, Hieu Phan Trung
{"title":"A Final Value Problem for the Nonlinear Modified Helmholtz Equation Associated with the Nonlinear Wave Velocity","authors":"Long Pham Nguyen Hoang,&nbsp;Triet Le Minh,&nbsp;Phong Luu Hong,&nbsp;Hieu Phan Trung","doi":"10.1007/s10440-025-00745-7","DOIUrl":"10.1007/s10440-025-00745-7","url":null,"abstract":"<div><p>This study focuses on the development and analysis of the backward problem for the nonlinear modified Helmholtz equation associated with nonlinear wave velocity. The governing equation is given as follows </p><div><div><span>$$triangle uleft ( x,yright ) -kleft ( l_{0}left ( uright ) left ( yright ) right ) uleft ( x,yright ) =Sleft ( x,y,uleft ( x,yright ) right ) ,~xin Omega ,~0&lt; y&lt; L. $$</span></div></div><p> To overcome the ill-posseness of the above problem, we apply the variational quasi-reversibility method. It is imperative to investigate the convergence analysis of this regularization method when we do not determine a formula of the exact solution. In this regard, we construct the approximate problem by adding the so-called perturbing operator to the original problem and by exploiting the Fourier reconstructed the final data. Then, we obtain the Hölder convergence rate of the proposed scheme under some certain assumptions on the exact solution. Finally, a numerical example is provided to corroborate the theoretical results.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"199 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110471","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
A Comprehensive Study on Symmetry and New Exact Solutions for (3 + 1) – Dimensional Mikhailov-Novikov-Wang Equation （3 + 1）维Mikhailov-Novikov-Wang方程对称性及新精确解的综合研究
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2025-09-15 DOI: 10.1007/s10440-025-00744-8
Ashutosh Kumar Karna, Purnima Satapathy
{"title":"A Comprehensive Study on Symmetry and New Exact Solutions for (3 + 1) – Dimensional Mikhailov-Novikov-Wang Equation","authors":"Ashutosh Kumar Karna,&nbsp;Purnima Satapathy","doi":"10.1007/s10440-025-00744-8","DOIUrl":"10.1007/s10440-025-00744-8","url":null,"abstract":"<div><p>This article investigates new exact solutions for the (3 + 1)–dimensional Mikhailov-Novikov-Wang equation, an extension of the (1 + 1)–dimensional Mikhailov-Novikov-Wang equation, which is notable for its connection to higher symmetries and the Boussinesq equation, complete integrability. While the Mikhailov-Novikov-Wang equation has been extensively studied and shown to be integrable with multiple soliton solutions, recent research has extended this to higher dimensions. The extended Mikhailov-Novikov-Wang equation has been found to be Painlevé integrable, yielding various soliton solutions such as rational, periodic, and kink-type solitons. Interestingly, while previous literature has primarily focused on soliton solutions, a comprehensive symmetry analysis of the equation remains unexplored to best of our knowledge. Here, we provide thorough exploration of the symmetries of the equation, including both classical and non-classical symmetries. By utilizing these symmetries, we are able to obtain exact solutions and illustrate them graphically, which enhances our comprehension of the dynamics of the equation.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"199 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145062288","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
Insights into Some Sets of (varepsilon )-Pseudo Fredholm Operators 一些(varepsilon ) -伪Fredholm算子集的见解
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2025-09-08 DOI: 10.1007/s10440-025-00743-9
Naila Bouida, Ines Walha
{"title":"Insights into Some Sets of (varepsilon )-Pseudo Fredholm Operators","authors":"Naila Bouida,&nbsp;Ines Walha","doi":"10.1007/s10440-025-00743-9","DOIUrl":"10.1007/s10440-025-00743-9","url":null,"abstract":"<div><p>One of the popular generalizations of the classical notion of essential spectra is the notion of pseudo essential spectra. The study around such notion has gained intensive interest in many research fields, particularly, in the theory of Fredholm operators. So, the novelty of our work is to develop a new sufficient criteria linked to the notion of <span>(Phi )</span>-perturbation function (recently invested by M. Mebekhta in (J. Oper. Theory 51:3–18, 2004)) allowing us to derive some new spectral analysis of some sets of <span>(varepsilon )</span>-pseudo Fredholm operators and their corresponding pseudo Weyl essential spectra. Moreover, our aim comes also to reach a new characterization in the setting of the so-called pseudo Weyl essential spectrum of a closed densely defined operator via the above approach of perturbation. Our results in this paper generalize and refine earlier work, particularly, the work done by S. Charfi et al. (Indag. Math. 28(3):670–679, 2017).</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"199 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145007944","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
Mathematical Modelling of Malaria Integrating Temperature, Rainfall, and Vegetation Index 结合温度、降雨和植被指数的疟疾数学模型
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2025-09-04 DOI: 10.1007/s10440-025-00740-y
Kelly Joëlle Gatore Sinigirira, Wandera Ogana, Faraimunashe Chirove
{"title":"Mathematical Modelling of Malaria Integrating Temperature, Rainfall, and Vegetation Index","authors":"Kelly Joëlle Gatore Sinigirira,&nbsp;Wandera Ogana,&nbsp;Faraimunashe Chirove","doi":"10.1007/s10440-025-00740-y","DOIUrl":"10.1007/s10440-025-00740-y","url":null,"abstract":"<div><p>Environmental factors such as temperature, rainfall, and vegetation index play a crucial role in the transmission dynamics of malaria. Accurately quantifying the complex relationships between these variables and the malaria burden poses a significant challenge. In this study, we developed a host-mosquito mathematical model to investigate the impact of temperature, rainfall, and normalized difference vegetation index (NDVI) on malaria transmission dynamics calibrated with the Burundi case’s study. Mathematical analysis explored the equilibria, stability, and computation of the model’s threshold values. Numerical simulations suggest that temperature, rainfall, and vegetation index affect the transmission dynamics of malaria. Temperature and NDVI appear to exhibit a more pronounced influence among these factors. The conditions conducive to malaria transmission include a mean monthly temperature range of [20-25 °C], an averaged monthly NDVI range of approximately [0.4-0.6]. The reproduction number was used as a quantitative measure to predict the impact of temperature, rainfall, and NDVI on malaria transmission dynamics across Burundi. The results suggest a progressive increase in the reproduction number over time, suggesting a threat of the rising number of cases in Burundi if drastic control measures are not implemented.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"199 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-025-00740-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fractional Quasilinear Hyperbolic Equations with Variable Sources 变源分数阶拟线性双曲方程
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2025-09-03 DOI: 10.1007/s10440-025-00741-x
Jiabin Zuo, J. Vanterler da C. Sousa, M. A. Pulido
{"title":"Fractional Quasilinear Hyperbolic Equations with Variable Sources","authors":"Jiabin Zuo,&nbsp;J. Vanterler da C. Sousa,&nbsp;M. A. Pulido","doi":"10.1007/s10440-025-00741-x","DOIUrl":"10.1007/s10440-025-00741-x","url":null,"abstract":"<div><p>In the present work, we are mainly concerned with some estimates related to the energy functional, in particular some uniform estimates of the solution decay rates. In this sense, we study the stable asymptotic behavior in terms of natural energy associated with the solution of a new class of fractional quasilinear hyperbolic equations with variable sources.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"199 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144929313","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
Dynamic Refinement of Pressure Decomposition in Navier-Stokes Equations Navier-Stokes方程压力分解的动态细化
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2025-09-03 DOI: 10.1007/s10440-025-00742-w
Pedro Gabriel Fernández-Dalgo
{"title":"Dynamic Refinement of Pressure Decomposition in Navier-Stokes Equations","authors":"Pedro Gabriel Fernández-Dalgo","doi":"10.1007/s10440-025-00742-w","DOIUrl":"10.1007/s10440-025-00742-w","url":null,"abstract":"<div><p>In this work, the local decomposition of pressure in the Navier-Stokes equations is dynamically refined to prove that a relevant critical energy of a Leray-type solution inside a backward paraboloid—regardless of its aperture—is controlled near the vertex by a critical behavior confined to a neighborhood of the paraboloid’s boundary. This neighborhood excludes the interior near the vertex and remains separated from the temporal profile of the vertex, except at the vertex itself. Moreover, we present a refined scaling-invariant regularity result.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"199 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144934774","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
Criteria of a Copositive Tensor with Application to Check Vacuum Stability of a General Scalar Potential 合张量的判据及其在检验一般标量势的真空稳定性中的应用
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2025-08-25 DOI: 10.1007/s10440-025-00739-5
Chunye Wang, Jianxing Zhao
{"title":"Criteria of a Copositive Tensor with Application to Check Vacuum Stability of a General Scalar Potential","authors":"Chunye Wang,&nbsp;Jianxing Zhao","doi":"10.1007/s10440-025-00739-5","DOIUrl":"10.1007/s10440-025-00739-5","url":null,"abstract":"<div><p>Existing literature shows that the vacuum stability of a general scalar potential is equivalent to the strict copositivity of its corresponding coupling tensor. In order to judge the copositivity of a coupling tensor, we provide two criteria of a strict copositive tensor, and show their correctness and effectiveness via two practical examples by checking the vacuum stability of a general scalar potential for <span>(mathbb{Z}_{3})</span> scalar dark matter.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"199 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144897203","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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