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Global Dynamics and Targeted Control of a Brucellosis Diffusion Model in Heterogeneous Environments 异质环境中布鲁氏菌病扩散模型的全局动力学和目标控制
IF 1.3 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-10-07 DOI: 10.1007/s10440-026-00811-8
Huining Wang, Yakui Xue, Boli Xie
{"title":"Global Dynamics and Targeted Control of a Brucellosis Diffusion Model in Heterogeneous Environments","authors":"Huining Wang,&nbsp;Yakui Xue,&nbsp;Boli Xie","doi":"10.1007/s10440-026-00811-8","DOIUrl":"10.1007/s10440-026-00811-8","url":null,"abstract":"<div><p>This study develops a reaction-diffusion model to investigate the transmission dynamics of brucellosis in a heterogeneous environment. We first establish the well-posedness of the system and derive the basic reproduction number <span>(R_{0})</span>. For the homogeneous case with heterogeneous diffusion, a complete global dynamical classification is established: the disease-free equilibrium is globally stable if <span>(R_{0} le 1)</span>, while the endemic equilibrium is globally asymptotically stable if <span>(R_{0} &gt; 1)</span>. Numerical simulations validate these theoretical results. Crucially, a global sensitivity analysis of <span>(R_{0})</span> identifies culling infected animals as the most effective single intervention for reducing transmission, outperforming vaccination and environmental disinfection. Based on this finding, we propose targeted control strategies, emphasizing that integrated measures—prioritizing early identification and culling of infected livestock—offer the most effective pathway for disease containment. This work provides both theoretical insights and practical guidance for optimizing brucellosis control.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"205 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132456","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
Viscous Profile of a Mixed Hyperbolic-Elliptic Problem: Existence and Uniqueness of the Solution of the Riemann Problem 混合双曲-椭圆问题的粘性剖面：黎曼问题解的存在唯一性
IF 1.3 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-10-05 DOI: 10.1007/s10440-026-00813-6
Mariam El-Abbassi, Chérif Ziti
{"title":"Viscous Profile of a Mixed Hyperbolic-Elliptic Problem: Existence and Uniqueness of the Solution of the Riemann Problem","authors":"Mariam El-Abbassi,&nbsp;Chérif Ziti","doi":"10.1007/s10440-026-00813-6","DOIUrl":"10.1007/s10440-026-00813-6","url":null,"abstract":"<div><p>In this paper, we investigate a class of Keller-Segel-type models that describe the chemotactic behavior of certain microorganisms. The resolution of the Riemann problem associated with such mixed-type hyperbolic-elliptic systems raises several challenges, including issues of existence, uniqueness, admissibility, and the appropriate selection of wave structures (shocks, rarefactions, contact discontinuities). For this type of system, classical admissibility criteria such as the Lax condition are insufficient to fully characterize the solution. To address this, we construct viscous shock profiles that allow us to rigorously establish the existence and uniqueness of an admissible solution. A detailed theoretical framework is developed to support the analysis.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"205 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132041","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
Analysis of a Chemotaxis SIR Reaction-Diffusion Model with Bilinear Incidence 一类双线性趋化SIR反应扩散模型的分析
IF 1.3 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-10-01 DOI: 10.1007/s10440-026-00812-7
Juan Gao, Hailiang Zhang
{"title":"Analysis of a Chemotaxis SIR Reaction-Diffusion Model with Bilinear Incidence","authors":"Juan Gao,&nbsp;Hailiang Zhang","doi":"10.1007/s10440-026-00812-7","DOIUrl":"10.1007/s10440-026-00812-7","url":null,"abstract":"<div><p>This paper introduces an SIR epidemic model that incorporates a bilinear chemotactic cross-diffusion mechanism, characterized by the avoidance of high-risk infected zones and the attraction to safer areas with recovered individuals. The model employs bilinear incidence rates to capture density-dependent transmission dynamics. Through rigorous mathematical analysis, we establish the global existence and boundedness of classical solutions under arbitrarily large initial data, provided the chemotactic sensitivity coefficients are sufficiently small. Furthermore, by constructing a Lyapunov functional, we demonstrate the global asymptotic stability of the disease-free equilibrium point <span>(left (frac{N}{|Omega |},0,0right ))</span>. High-resolution numerical simulations implemented via discretization methods quantify the evolutionary trajectories of model solutions and reveal strategic spatial intervention implications.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"205 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149132390","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
Random Additive Perturbation of a (k) Term Recurrence Relation (k)项递推关系的随机加性扰动
IF 1.3 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-09-30 DOI: 10.1007/s10440-026-00810-9
Lisette Jager, Killian Verdure
{"title":"Random Additive Perturbation of a (k) Term Recurrence Relation","authors":"Lisette Jager,&nbsp;Killian Verdure","doi":"10.1007/s10440-026-00810-9","DOIUrl":"10.1007/s10440-026-00810-9","url":null,"abstract":"<div><p>This paper deals with a real valued process driven by a general <span>(k)</span> term recurrence relation and perturbed by an additive random term. The first step is the case when the perturbation is a fixed constant <span>(theta )</span>. To get a transformation - which depends on this constant term - of a <span>(k)</span> dimensional space and apply classical techniques [24], we imbed the recurrence relation in <span>({mathbb{R}}^{k})</span> in a particular way, implying the use of a small parameter. We then study the transfer operator of the transformation, taking care of the uniformity with respect to the constant <span>(theta )</span>. The second step is the study of the perturbed process. Following [1], we introduce the expectation of the individual <span>(k)</span>-dimensional transfer operators studied before. This “averaged” transfer operator has a finite number of modulus 1 eigenvalues and a spectral gap. It admits an absolutely continuous invariant measure (ACIM) on <span>({mathbb{R}}^{k})</span>, which, in turn, gives an ACIM for the initial real valued process.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"205 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149133262","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
The Inhomogeneous Boltzmann Equation in a Bianchi Type I Space-Time for Hard Potentials 硬势的Bianchi I型时空非齐次玻尔兹曼方程
IF 1.3 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-09-22 DOI: 10.1007/s10440-026-00809-2
Emmanuel Tchuengue Kamdem, Etienne Takou
{"title":"The Inhomogeneous Boltzmann Equation in a Bianchi Type I Space-Time for Hard Potentials","authors":"Emmanuel Tchuengue Kamdem,&nbsp;Etienne Takou","doi":"10.1007/s10440-026-00809-2","DOIUrl":"10.1007/s10440-026-00809-2","url":null,"abstract":"<div><p>This paper investigates the inhomogeneous Boltzmann equation in a Bianchi type I space-time where the scattering kernel is for hard potentials. We have proved the global (with respect to the direction of time corresponding to the expansion of the universe) existence of classical solutions for small initial data in a suitable weighted space for some collisional kernel which fall in the class of hard potentials. Such kernels are closer to those which naturally arise in physical problems. Our result extends existing results such as the one for mild solutions and also the classical solution for Israel particles.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"205 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149034771","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
Large Time Solution via Blues Function Method for Non-linear Redner Ben Kahng Coagulation Model 非线性Redner Ben kahh凝固模型的布鲁斯函数法大时间解
IF 1.3 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-09-14 DOI: 10.1007/s10440-026-00808-3
Shweta Yadav, Rajesh Kumar
{"title":"Large Time Solution via Blues Function Method for Non-linear Redner Ben Kahng Coagulation Model","authors":"Shweta Yadav,&nbsp;Rajesh Kumar","doi":"10.1007/s10440-026-00808-3","DOIUrl":"10.1007/s10440-026-00808-3","url":null,"abstract":"<div><p>Population balance equations (PBEs) play a central role in describing the evolution of particle concentrations in a wide range of applications, including polymerisation processes, astrophysical clustering, nanoparticle synthesis, and pharmaceutical engineering. The nonlinear nature of these equations makes it challenging to obtain analytical solutions for physically relevant coagulation kernels. In this work, the continuous Redner-Ben-Avraham-Kahng (RBK) coagulation model is investigated using the Beyond Linear Use of Equation Superposition (BLUES) function method. The proposed framework extends the BLUES methodology to the continuous RBK coagulation equation and provides an efficient semi-analytical approach for computing particle concentrations and their integral moments. Its performance is assessed through comparisons with available analytical solutions, the homotopy perturbation method (HPM), the accelerated homotopy perturbation method (AHPM), and, where exact solutions are unavailable, the finite volume method (FVM). The results demonstrate that the proposed method achieves higher accuracy and faster convergence than existing semi-analytical approaches, particularly over extended time intervals. Furthermore, rigorous convergence and error analyses establish the theoretical reliability of the proposed iterative scheme.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"205 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148986234","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
Nonlinear Distortion of Symmetry in Solutions to the Convection-Diffusion Equation of Burgers Type Burgers型对流扩散方程解对称性的非线性畸变
IF 1.3 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-09-01 DOI: 10.1007/s10440-026-00806-5
Masakazu Yamamoto
{"title":"Nonlinear Distortion of Symmetry in Solutions to the Convection-Diffusion Equation of Burgers Type","authors":"Masakazu Yamamoto","doi":"10.1007/s10440-026-00806-5","DOIUrl":"10.1007/s10440-026-00806-5","url":null,"abstract":"<div><p>In this paper, the initial value problem of the convection-diffusion equation of Burgers type is treated. In the asymptotic profile of solutions, the nonlinearity of the equation is reflected. Regarding the solutions to this model, the Spanish school in the 1990s performed asymptotic expansions based on the linear diffusion. Those profiles exhibit symmetries characteristic of linear phenomena. In this paper, the distortion of symmetry arising from the nonlinear effects is described explicitly. Furthermore, it is demonstrated that the extent of this distortion differs significantly depending on the parity of the spatial dimension. This contradicts the conventional expectation that the manifestation of nonlinearity depends on the scale of the equation. This interpretation is supported by comparison with similar Navier–Stokes equations. The Burgers type is applicable as an indicator for considering several bilinear problems.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"205 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926487","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
Motion of Elastic Thin Films by Evaporation-Condensation in the Dewetting Regime 弹性薄膜在脱湿状态下的蒸发-冷凝运动
IF 1.3 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-09-01 DOI: 10.1007/s10440-026-00807-4
M. S. Indulekha
{"title":"Motion of Elastic Thin Films by Evaporation-Condensation in the Dewetting Regime","authors":"M. S. Indulekha","doi":"10.1007/s10440-026-00807-4","DOIUrl":"10.1007/s10440-026-00807-4","url":null,"abstract":"<div><p>In this work, we show the short-time existence of solutions of the evolution equations that represent the solid state dewetting of thin films through evaporation-condensation as a two dimensional sharp interface variational model. The evolution law is established as the <span>(L^{2})</span> gradient flow of surface energies in the presence of epitaxial strain. The main novelty is the presence of moving contact lines when the film formation is governed by the evaporation-condensation method.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"205 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-026-00807-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926488","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
Existence of a Solution for a Class of Kirchhoff-Boussinesq Type Equations with Potential Changing Signs 一类具有势变符号的Kirchhoff-Boussinesq型方程解的存在性
IF 1.3 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-08-19 DOI: 10.1007/s10440-026-00804-7
Romulo D. Carlos, Giovany M. Figueiredo, Ricardo Ruviario
{"title":"Existence of a Solution for a Class of Kirchhoff-Boussinesq Type Equations with Potential Changing Signs","authors":"Romulo D. Carlos,&nbsp;Giovany M. Figueiredo,&nbsp;Ricardo Ruviario","doi":"10.1007/s10440-026-00804-7","DOIUrl":"10.1007/s10440-026-00804-7","url":null,"abstract":"<div><p>This paper is concerned with the existence of a ground state solution for the following class of elliptic Kirchhoff-Boussinesq type problems given by </p><div><div><span>$$ Delta ^{2} u pm Delta _{p} u + V(x)u= f(u) +gamma |u|^{2_{**}-2}u text{in} mathbb{R}^{N}, $$</span></div></div><p> where <span>(2&lt; pleq 2^{*}= frac{2N}{N-2})</span> for <span>(Ngeq 5)</span> and <span>(2_{**}= frac{2N}{N-4})</span>. The potential <span>(V)</span> can change sign and <span>(f)</span> is a continuous function with subcritical growth and behaves like <span>(|u|^{q-2}u)</span> with <span>(p&lt; q&lt; 2_{**})</span>. We show the existence of a ground state solution using variational methods, Splitting Lemma and considering the subcritical case, i.e, <span>(gamma =0)</span> and the critical case, i.e, <span>(gamma =1)</span>.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"205 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-026-00804-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782923","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
Delta-Shocks to Non-homogeneous Euler Equations with Varying Chaplygin Gas 变化Chaplygin气体的非齐次欧拉方程的δ激波
IF 1.3 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-08-15 DOI: 10.1007/s10440-026-00805-6
Huixu Li, Shiwei Li
{"title":"Delta-Shocks to Non-homogeneous Euler Equations with Varying Chaplygin Gas","authors":"Huixu Li,&nbsp;Shiwei Li","doi":"10.1007/s10440-026-00805-6","DOIUrl":"10.1007/s10440-026-00805-6","url":null,"abstract":"<div><p>The Riemann problem for the varying Chaplygin gas Euler equations with zeroth-order terms is investigated. By the varying Chaplygin gas, we mean that the fluid obeys the pressure-density-time relation where the pressure is negative and is the product of a function of time and the inverse of the density. It includes the Chaplygin gas as an exceptional case. Through the variable substitution method, the solution formed by two contact discontinuities and the solution with delta-shock are constructed in completely explicit forms. Under the generalized Rankine-Hugoniot relation and entropy condition, the position, propagation speed and strength of the delta-shock are uniquely determined. It is discovered that the shape of delta-shock in characteristic plane is either an exponential type curve or a straight line. An interesting phenomenon concerning the delta-shock is that even when the delta-shock is a straight line, its weight is no longer linear function of time. The phenomenon is attributed to the presence of the mass source term. It means that mass source term can play a role in adjusting the weight of the delta-shock. Additionally, it is proved that the constructed Riemann solutions tend to those of nonhomogeneous zero-pressure Euler equations with the same initial data as varying Chaplygin gas tends to zero, and the constructed Riemann solutions converge to the corresponding ones of Chaplygin gas Euler equations with same initial data as both source terms vanish simultaneously.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"204 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782150","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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