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The Limiting Behavior of the Riemann Solutions to the Eulerian Droplet Model with Varying Generalized Chaplygin Gas 变广义Chaplygin气体欧拉液滴模型黎曼解的极限行为
IF 1.3 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-08-13 DOI: 10.1007/s10440-026-00803-8
Yanyan Zhang, Wenshuai Fu
{"title":"The Limiting Behavior of the Riemann Solutions to the Eulerian Droplet Model with Varying Generalized Chaplygin Gas","authors":"Yanyan Zhang,&nbsp;Wenshuai Fu","doi":"10.1007/s10440-026-00803-8","DOIUrl":"10.1007/s10440-026-00803-8","url":null,"abstract":"<div><p>We consider the Eulerian droplet model with a varying generalized Chaplygin gas, which possesses negative pressure and is a product of a function of time and the inverse of a power of the density. The non-self-similar Riemann solutions are obtained, and then the limiting behavior of the Riemann solutions is investigated. As the parameter decreases to a critical value, the two-shock solution converges to a delta shock wave of the same system. Further, when the parameter goes to zero(vanishing pressure), the solution becomes exactly the delta shock wave solution of the zero-pressure Eulerian droplet model. Moreover, the two-rarefaction wave solution tends to a solution consisting of four contact discontinuities together with vacuum states, which is different from the vacuum solution of the zero-pressure Eulerian droplet model. The solution containing one rarefaction wave and one shock wave tends to the contact discontinuity solution of the zero-pressure Eulerian droplet model as pressure vanishes.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"204 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751798","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
Dynamics of Population Growth in Nicholson’s Blowflies Biology Model: New Results on Pseudo-Compact Almost-Automorphy Nicholson苍蝇生物学模型中种群增长的动态：关于伪紧致几乎自同构的新结果
IF 1.3 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-08-11 DOI: 10.1007/s10440-026-00802-9
Moez Ayachi
{"title":"Dynamics of Population Growth in Nicholson’s Blowflies Biology Model: New Results on Pseudo-Compact Almost-Automorphy","authors":"Moez Ayachi","doi":"10.1007/s10440-026-00802-9","DOIUrl":"10.1007/s10440-026-00802-9","url":null,"abstract":"<div><p>This work focuses on Nicholson’s blowflies model with mixed time-varying delays, a non-linear Immigration term, and <span>((varsigma _{1},varsigma _{2}))</span>-pseudo-compact almost-automorphic parameters. The main contribution consists of improving and generalizing some existing results about <span>((varsigma _{1},varsigma _{2}))</span>-pseudo compact almost-automorphic functions. Then, based on differential inequalities, the fixed point theorem, and the Halanay inequality, we establish some sufficient conditions for the existence, stability, and attractivity of positive solutions for the model considered. Further, we present a numerical example to support and illustrate the theoretical findings. Finally, a conclusion is drawn. Our findings are new and extend some existing results in the literature.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"204 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148751454","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 New Semi-Analytic Algorithm of Nearly Singular Integrals with Various Kernels in BEM for Analyzing 2D Elasticity Problems 二维弹性问题边界元中多核近奇异积分的一种新的半解析算法
IF 1.3 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-07-13 DOI: 10.1007/s10440-026-00801-w
Weicheng Lin, Chuanming Ju, Xin Wang, Jiehao Chen, Shuangyu Yu
{"title":"A New Semi-Analytic Algorithm of Nearly Singular Integrals with Various Kernels in BEM for Analyzing 2D Elasticity Problems","authors":"Weicheng Lin,&nbsp;Chuanming Ju,&nbsp;Xin Wang,&nbsp;Jiehao Chen,&nbsp;Shuangyu Yu","doi":"10.1007/s10440-026-00801-w","DOIUrl":"10.1007/s10440-026-00801-w","url":null,"abstract":"<div><p>The accuracy of evaluating nearly singular integrals is crucial to determining the accuracy and stability of BEM in solving elastic problems. A novel semi-analytic method is developed for calculating nearly singular integrals with various kernel functions. Different from the traditional semi-analytical method, the Taylor expansion for shape functions, Jacobian, and so on in our method is based on the nearest point from a source point to an integral element rather than the projection point from the source point to the integral element. Therefore, it can more accurately approximate the distance from the source point to Gaussian integration points. Based on these Taylor expansions, approximate expressions for the integrand functions of two-dimensional elastic problems are derived. The effectiveness of this method is demonstrated by evaluating the accuracy of physical quantities at various points within different geometric models and comparing the results with those of the traditional semi-analytic method and the distance transformation method.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"204 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465677","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
Theoretical and Numerical Analysis of 2D Fractional Volterra-Fredholm Integro-Differential Equations with Applications to Image Enhancement 二维分数阶Volterra-Fredholm积分微分方程的理论与数值分析及其在图像增强中的应用
IF 1.3 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-07-07 DOI: 10.1007/s10440-026-00799-1
Bapan Ali Miah, Mausumi Sen, R. Murugan
{"title":"Theoretical and Numerical Analysis of 2D Fractional Volterra-Fredholm Integro-Differential Equations with Applications to Image Enhancement","authors":"Bapan Ali Miah,&nbsp;Mausumi Sen,&nbsp;R. Murugan","doi":"10.1007/s10440-026-00799-1","DOIUrl":"10.1007/s10440-026-00799-1","url":null,"abstract":"<div><p>This study investigates the existence and uniqueness of solutions for a class of two-dimensional fractional-order Volterra-Fredholm integro-differential equations (2D-FVFIDEs). The Krasnoselskii fixed-point theorem is employed to prove the existence of solutions, while Banach’s fixed-point theorem is used to establish their uniqueness. To compute numerical solutions, we adopt the discrete Laplace-Adomian Decomposition Method (LADM), which effectively handles the complexities introduced by fractional and integral operators. A series of illustrative numerical examples validate the theoretical results and demonstrate the robustness of the proposed approach. We have also compared the numerical results with those obtained using existing methods. Moreover, the developed integro-differential model is applied to the field of image processing for enhancement tasks. The model’s practical utility is showcased through experiments on various medical and real-time images, confirming its potential in real-world applications.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"204 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148465143","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 Global Existence of Bounded Weak Solutions to a Degenerate Haptotaxis and Diffusion Model of Cancer Invasion 一类退化肿瘤侵袭趋合扩散模型有界弱解的整体存在性
IF 1.3 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-07-03 DOI: 10.1007/s10440-026-00798-2
B. Price, X. Xu
{"title":"The Global Existence of Bounded Weak Solutions to a Degenerate Haptotaxis and Diffusion Model of Cancer Invasion","authors":"B. Price,&nbsp;X. Xu","doi":"10.1007/s10440-026-00798-2","DOIUrl":"10.1007/s10440-026-00798-2","url":null,"abstract":"<div><p>In this paper we study a haptotaxis and diffusion model of cancer invasion. The model consists of a parabolic PDE coupled with an ODE. The PDE itself contains the gradients of both unknowns, as well as well as the potential to be degenerate. This degeneracy appearing in the PDE provides the main source of difficulty for this system. We derive new estimates showing solutions must be bounded which then enable us to prove the global existence of weak solutions.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"204 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148365991","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
Well–Posedness and Averaging for the Dispersion–Managed NLS in (H^{m}) 分散管理NLS的适定性和平均 (H^{m})
IF 1.3 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-07-03 DOI: 10.1007/s10440-026-00800-x
Mi-Ran Choi, Dugyu Kim
{"title":"Well–Posedness and Averaging for the Dispersion–Managed NLS in (H^{m})","authors":"Mi-Ran Choi,&nbsp;Dugyu Kim","doi":"10.1007/s10440-026-00800-x","DOIUrl":"10.1007/s10440-026-00800-x","url":null,"abstract":"<div><p>This paper studies the well–posedness and averaging for the dispersion–managed nonlinear Schrödinger equation (NLS) with general nonlinearity, where the dispersion map <span>(gamma )</span> is assumed to be piecewise constant. We establish the local well–posedness of the equation in the Sobolev space <span>(H^{m}(mathbb{R}^{N}))</span> by applying a fixed–point theorem. Furthermore, we analyze the convergence of the solutions of the original equation to the solutions of the averaged equation. The analysis relies on linear propagators and Strichartz estimates to derive the main results. This study helps us improve our understanding of the dynamic behavior of dispersion–managed NLS and provides a mathematical framework that can be used in different physical systems.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"204 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148365990","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 Incompressible Limit of an Inhomogeneous Model of Tissue Growth 组织生长的非均匀模型的不可压缩极限
IF 1.3 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-06-14 DOI: 10.1007/s10440-026-00797-3
Anthony Sulak, Olga Turanova
{"title":"The Incompressible Limit of an Inhomogeneous Model of Tissue Growth","authors":"Anthony Sulak,&nbsp;Olga Turanova","doi":"10.1007/s10440-026-00797-3","DOIUrl":"10.1007/s10440-026-00797-3","url":null,"abstract":"<div><p>We study a porous medium equation that models tissue growth in a heterogeneous environment. We show that, in the incompressible limit, solutions converge to those of a weak form of a Hele-Shaw type free boundary problem. To obtain enough compactness to take the limit, we establish an <span>(L^{4})</span> bound on the gradient of the pressure and an estimate of Aronson-Bénilan type.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"203 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2026-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-026-00797-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148281228","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
Glutamate-GABA Cross-Diffusion Dynamics in a Networked Gierer-Meinhardt Model 网络Gierer-Meinhardt模型中的谷氨酸-氨基丁酸交叉扩散动力学
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-06-04 DOI: 10.1007/s10440-026-00796-4
Zhi Ling, Shuxian Tang, Canrong Tian, You Zhou
{"title":"Glutamate-GABA Cross-Diffusion Dynamics in a Networked Gierer-Meinhardt Model","authors":"Zhi Ling,&nbsp;Shuxian Tang,&nbsp;Canrong Tian,&nbsp;You Zhou","doi":"10.1007/s10440-026-00796-4","DOIUrl":"10.1007/s10440-026-00796-4","url":null,"abstract":"<div><p>This study proposes a neural networked Gierer-Meinhardt model to characterize the spatiotemporal dynamics of glutamate and <span>(gamma)</span>-aminobutyric acid (GABA) by incorporating both free-diffusion and cross-diffusion mechanisms. The primary objective is to investigate whether diffusive terms can destabilize an initially stable Hopf bifurcation periodic solution and subsequently trigger the emergence of irregular spatiotemporal patterns. Using Floquet multiplier analysis, we rigorously evaluate the potential of diffusion-driven perturbations to disrupt the periodic solution, thereby establishing a quantitative basis for identifying the onset of diffusion-induced pattern formation. Numerical simulations confirm our theoretical predictions and further explore the effect of networked cross-diffusion on the dynamics. By integrating reaction-diffusion dynamics with network topology, this framework provides a mathematical foundation for analyzing the interplay between excitatory and inhibitory neurotransmitter models in neural networks and their role in spatiotemporal pattern formations.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"203 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172324","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
Explicit Bounds on the Energy and Moduli of a Composite Elastic Plate 复合弹性板的能量和模量的显式界限
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-06-02 DOI: 10.1007/s10440-026-00794-6
Krešimir Burazin, Jelena Jankov Pavlović
{"title":"Explicit Bounds on the Energy and Moduli of a Composite Elastic Plate","authors":"Krešimir Burazin,&nbsp;Jelena Jankov Pavlović","doi":"10.1007/s10440-026-00794-6","DOIUrl":"10.1007/s10440-026-00794-6","url":null,"abstract":"<div><p>In this paper we consider the fourth-order elliptic equation describing the Kirchhoff-Love model for pure bending of a thin solid symmetric plate under a transverse load. We derive Hashin-Shtrikman bounds on the complementary energy, and calculate these bounds explicitly for mixtures of two isotropic materials in dimension <span>(d=2)</span>. Moreover, we give bounds on the bulk and shear moduli of an isotropic two-phase composite material, and show that these bounds are optimal, i.e. that they are attainable by finite-rank sequential laminates. These results pave the way for numerous applications of the homogenization theory in optimal design problems for stationary elastic plates, for example the development of an optimality criteria method for two-dimensional compliance minimization problems.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"203 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172352","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
Well-Posedness and Global Stabilization of an Euler-Bernoulli Beam with Distributed Damping and Nonlinear Boundary Delay 具有分布阻尼和非线性边界延迟的Euler-Bernoulli梁的适定性和全局镇定性
IF 1 4区 数学
Acta Applicandae Mathematicae Pub Date : 2026-06-01 DOI: 10.1007/s10440-026-00795-5
Nizar Mahfoudhi, Habib Ayadi
{"title":"Well-Posedness and Global Stabilization of an Euler-Bernoulli Beam with Distributed Damping and Nonlinear Boundary Delay","authors":"Nizar Mahfoudhi,&nbsp;Habib Ayadi","doi":"10.1007/s10440-026-00795-5","DOIUrl":"10.1007/s10440-026-00795-5","url":null,"abstract":"<div><p>This paper addresses the problems of global well-posedness and asymptotic stabilization for a viscoelastic Euler-Bernoulli beam model incorporating distributed damping and a nonlinear feedback with time delay acting at the right boundary as a shear force. The nonlinearity is merely assumed to be Lipschitz continuous and to vanish at the origin, without satisfying boundedness or monotonicity as in saturation or cone-bounded cases. By a change of variables to handle the delay, the system is reformulated as an evolutionary coupled beam-transport system in a suitable Hilbert space. We then show that the corresponding nonlinear operator generates a contraction semigroup, ensuring the global well-posedness of the system. Furthermore, by designing an appropriate Lyapunov functional and applying LaSalle’s invariance principle in infinite dimension, we establish the global asymptotic stability of the system. This work extends existing results by effectively addressing the complex interaction between a distributed damping mechanism, a broad class of nonlinearities, and a boundary time delay. A numerical simulation validating the proposed approach is provided.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"203 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172550","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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