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Global Existence of Weak Solution for the 2D Chemotaxis-Navier-Stokes Equations with Arbitrary Porous Medium Diffusion 具有任意多孔介质扩散的二维chemotaxi - navier - stokes方程弱解的整体存在性
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-03-23 DOI: 10.1007/s10440-026-00783-9
Mingxi Li, Qian Zhang
{"title":"Global Existence of Weak Solution for the 2D Chemotaxis-Navier-Stokes Equations with Arbitrary Porous Medium Diffusion","authors":"Mingxi Li,&nbsp;Qian Zhang","doi":"10.1007/s10440-026-00783-9","DOIUrl":"10.1007/s10440-026-00783-9","url":null,"abstract":"<div><p>We consider the Cauchy problem for chemotaxis-Navier-Stokes equations with nonlinear diffusion <span>(Delta n^{m})</span> in <span>(mathbb{R}^{2})</span>. By exploring the new a priori estimates, we establish the global existence of weak solutions to the chemotaxis-Navier-Stokes equations with <span>(m&gt;1)</span>. This result extends the bounded domain in reference (Tao and Winkler in Discrete Contin. Dyn. Syst. 32:1901–1914, 2012) to the entire space.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"202 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561119","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, Uniqueness, and Stability Analysis Results for an Epidemic Model with Piecewise Constant Delay of Generalized Type 一类广义型分段常时滞流行病模型的存在唯一性及稳定性分析结果
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-03-23 DOI: 10.1007/s10440-026-00782-w
Kuo-Shou Chiu
{"title":"Existence, Uniqueness, and Stability Analysis Results for an Epidemic Model with Piecewise Constant Delay of Generalized Type","authors":"Kuo-Shou Chiu","doi":"10.1007/s10440-026-00782-w","DOIUrl":"10.1007/s10440-026-00782-w","url":null,"abstract":"<div><p>This study investigates an epidemic framework governed by differential equations featuring delays of generalized piecewise constant structure (DEGPCD). The primary objective is to construct an invariant region and to demonstrate the existence and uniqueness of solutions by employing integral equation techniques under appropriately defined conditions. Additionally, an auxiliary lemma is derived, establishing a precise connection between the functional values of the state variable within the delay argument and the temporal domain. To investigate the model’s dynamic behavior, the Lyapunov–Razumikhin framework is utilized, tailored to accommodate the structural features introduced by the DEGPCD. The stability of the infection-free state is rigorously examined, while the positive steady state is transformed into an equivalent zero equilibrium to facilitate the analysis. Sufficient criteria are then formulated to guarantee uniform asymptotic stability for both equilibria, offering theoretical insights that enhance the applicability of DEGPCD-based epidemic modeling.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"202 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-03-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147561122","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
New and Old Links Between PDEs and Voronoi Patterns pde与Voronoi模式之间的新旧联系
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-03-17 DOI: 10.1007/s10440-026-00779-5
Yuriria Cortés-Poza, David Padilla-Garza, Pablo Padilla-Longoria
{"title":"New and Old Links Between PDEs and Voronoi Patterns","authors":"Yuriria Cortés-Poza,&nbsp;David Padilla-Garza,&nbsp;Pablo Padilla-Longoria","doi":"10.1007/s10440-026-00779-5","DOIUrl":"10.1007/s10440-026-00779-5","url":null,"abstract":"<div><p>This paper presents a range of results in partial differential equations (PDEs) in which Voronoi patterns arise. Some are well-known and are presented here for the sake of completeness. Others are intuitive, but their proofs are not necessarily simple and are not found in the literature. We also introduce some new connections between Voronoi patterns and PDEs. We first investigate the connection between Voronoi tessellations and the solution to an elliptic equation and its probabilistic interpretation as a stochastic colonization game. An agent-based model is designed and implemented to generate Voronoi cells, motivated by experimental results with bacteria and chemical reactions, emulating this colonization game. We also consider the analytical solution to a related elliptic problem, which enables us to define what we call a harmonic Voronoi tessellation. We analyze parabolic equations in Riemannian manifolds, which have criticalapplications in chemical reactions and diffusive fronts. Using short-timeheat kernel estimates, we demonstrate that the interaction of <span>(n)</span> pointsources gives rise to a Voronoi tessellation. We recall some well-known results of wavefront interactions from point light sources and the Huygens principle. We apply results on the particular set of weak solutions to the eikonal equation to characterize Voronoi patterns arising in this context as rectifiable sets. Finally, we present an optimal transport problem and the corresponding Monge-Ampère equation, in which a uniform measure is transported to a sum of <span>(n)</span> Dirac masses with a cost given by the Euclidean distance. These problems are naturally linked to power sets, a generalization of Voronoi tessellations.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"202 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-03-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-026-00779-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147559298","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
Approximate Controllability of Fractional Differential Systems of (psi )-Caputo Type with Delay in State 状态时滞(psi ) -Caputo型分数阶微分系统的近似可控性
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-03-12 DOI: 10.1007/s10440-026-00778-6
Dibyajyoti Hazarika, Jayanta Borah, Bhupendra Kumar Singh
{"title":"Approximate Controllability of Fractional Differential Systems of (psi )-Caputo Type with Delay in State","authors":"Dibyajyoti Hazarika,&nbsp;Jayanta Borah,&nbsp;Bhupendra Kumar Singh","doi":"10.1007/s10440-026-00778-6","DOIUrl":"10.1007/s10440-026-00778-6","url":null,"abstract":"<div><p>In this article we investigate the approximate controllability results for delay fractional differential evolution systems with <span>(psi )</span>-Caputo fractional derivative. We derive sufficient conditions to establish the approximate controllability of the system with the help of the un-delayed corresponding system. Also the existence, uniqueness and boundedness of the mild solutions of the said systems are proved using Banach contraction principle. An example is provided at the end to validate the results.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"202 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147441578","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
Stability of Riemann Solutions for an Inhomogeneous Keyfitz-Kranzer System with Chaplygin Gas Pressure 具有Chaplygin气体压力的非齐次Keyfitz-Kranzer系统Riemann解的稳定性
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-03-05 DOI: 10.1007/s10440-026-00777-7
Mengqi Cui, Yanyan Zhang, Yu Zhang
{"title":"Stability of Riemann Solutions for an Inhomogeneous Keyfitz-Kranzer System with Chaplygin Gas Pressure","authors":"Mengqi Cui,&nbsp;Yanyan Zhang,&nbsp;Yu Zhang","doi":"10.1007/s10440-026-00777-7","DOIUrl":"10.1007/s10440-026-00777-7","url":null,"abstract":"<div><p>The structural stability of Riemann solutions for a kind of Keyfitz-Kranzer (K-K) system with Chaplygin gas pressure and time-dependent source term is studied by the method of perturbation of initial value. It is rigorously proved that, as the perturbed parameter <span>(varepsilon )</span> tends to zero, no mass concentration will happen even the initial perturbed density depends on <span>(varepsilon )</span>, which implies that the Riemann solutions of the K-K system are stable under the local small perturbation of the initial data.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"202 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147352815","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 Fast Forward-Backward Splitting Method for Nonmonotone Inclusions 非单调包含的快速前向后分裂方法
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-02-11 DOI: 10.1007/s10440-026-00776-8
Thanh Quoc Trinh, Tuan Anh Pham, Van Dung Nguyen
{"title":"A Fast Forward-Backward Splitting Method for Nonmonotone Inclusions","authors":"Thanh Quoc Trinh,&nbsp;Tuan Anh Pham,&nbsp;Van Dung Nguyen","doi":"10.1007/s10440-026-00776-8","DOIUrl":"10.1007/s10440-026-00776-8","url":null,"abstract":"<div><p>In this paper, we design a new splitting method for solving nonmonotone inclusions in Hilbert spaces. Our method incorporates an inertial term, and a correction term into the forward-backward algorithm. The weak convergence of the sequence of iterations is derived, with worst-case rates of <span>(o(k^{-1}))</span> in terms of both the discrete velocity and the fixed point residual. The new method recovers the method in the literature as a special case. We also give some numerical experiments to demonstrate the efficiency of the proposed method.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"201 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147338834","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
Time-Dependent Positively Invariant Sets on Cauchy Problems: Applications in Population Dynamics 柯西问题上的时相关正不变集：在种群动力学中的应用
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-02-10 DOI: 10.1007/s10440-026-00775-9
Moustapha Dieye, Ramsès Djidjou-Demasse, Ousmane Seydi
{"title":"Time-Dependent Positively Invariant Sets on Cauchy Problems: Applications in Population Dynamics","authors":"Moustapha Dieye,&nbsp;Ramsès Djidjou-Demasse,&nbsp;Ousmane Seydi","doi":"10.1007/s10440-026-00775-9","DOIUrl":"10.1007/s10440-026-00775-9","url":null,"abstract":"<div><p>We establish flow invariance results for semilinear systems governed by non-Hille–Yosida operators under time-dependent closed convex constraints. A new subtangential condition is introduced, together with explicit sufficient conditions for positive invariance formulated in terms of the resolvent and the nonlinear term. The results apply to systems with non-densely defined operators and time-varying constraints, and are illustrated by applications to an age-structured predator–prey model, a biofilm model, and a class of neutral functional differential equations.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"201 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-026-00775-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147338240","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
Controllability Results for Impulsive Atangana-Baleanu Fractional Stochastic Differential Systems with Second-Order Hermite Process 二阶Hermite过程脉冲Atangana-Baleanu分数阶随机微分系统的可控性结果
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-02-10 DOI: 10.1007/s10440-026-00773-x
Rajesh Dhayal, J. F. Gómez-Aguilar, Eduardo Pérez-Careta
{"title":"Controllability Results for Impulsive Atangana-Baleanu Fractional Stochastic Differential Systems with Second-Order Hermite Process","authors":"Rajesh Dhayal,&nbsp;J. F. Gómez-Aguilar,&nbsp;Eduardo Pérez-Careta","doi":"10.1007/s10440-026-00773-x","DOIUrl":"10.1007/s10440-026-00773-x","url":null,"abstract":"<div><p>This paper develops a new class of impulsive Atangana-Baleanu fractional stochastic differential systems with the Rosenblatt process, which is a Hermite process of order two with long-range dependence and stationary increments properties. Firstly, we established the existence of solutions to the considered problem by using the fixed point technique, resolvent family, and fractional calculus. Then, we discussed the controllability results for the proposed system. Finally, an illustrative example is given to demonstrate the obtained results.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"201 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147338239","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
Error Analysis of a Frictional Piezoelectric Contact Problem 压电摩擦接触问题的误差分析
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-02-03 DOI: 10.1007/s10440-026-00774-w
H. El Khalfi, Z. Faiz, A. Oultou, H. Benaissa
{"title":"Error Analysis of a Frictional Piezoelectric Contact Problem","authors":"H. El Khalfi,&nbsp;Z. Faiz,&nbsp;A. Oultou,&nbsp;H. Benaissa","doi":"10.1007/s10440-026-00774-w","DOIUrl":"10.1007/s10440-026-00774-w","url":null,"abstract":"<div><p>In this work, a particular class of penalized Signorini’s models with a normal compliance contact condition is studied. These contact models are created by taking two parameters: a power parameter <span>(alpha geq 1)</span> and a punishment parameter <span>(varepsilon )</span>. A standard penalization is represented by a value of <span>(alpha =1)</span>. These contact models function as nonlinear approximations for Signorini’s problem. Choosing a continuous, conforming linear finite element approximation is the first step in our method. We then calculate <span>(L^{2})</span>-error estimates with suitable assumptions, which are carefully examined and explained.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"201 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147336503","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
Global Existence and Temporal Decay for the 3D Magneto-Viscoelastic Fluids 三维磁粘弹性流体的全局存在性和时间衰减
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-02-02 DOI: 10.1007/s10440-026-00772-y
Chengling Li, Qiao Liu
{"title":"Global Existence and Temporal Decay for the 3D Magneto-Viscoelastic Fluids","authors":"Chengling Li,&nbsp;Qiao Liu","doi":"10.1007/s10440-026-00772-y","DOIUrl":"10.1007/s10440-026-00772-y","url":null,"abstract":"<div><p>This paper concerns the Cauchy problem of the 3D magneto-viscoelastic fluids. Using the pure energy method, we prove the global well-posedness of the classical solutions with smooth initial data of small <span>(L^{2})</span> energy. Furthermore, under some additional assumptions on the initial data, we obtain the algebraic temporal decay rates of the higher-order spatial derivatives of solutions.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"201 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147336208","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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