Acta Applicandae Mathematicae最新文献

{"title":"Dissipation Through Combinations of Nonlocal and Gradient Nonlinearities in Chemotaxis Models","authors":"Rafael Díaz Fuentes,&nbsp;Silvia Frassu,&nbsp;Giuseppe Viglialoro","doi":"10.1007/s10440-025-00714-0","DOIUrl":"10.1007/s10440-025-00714-0","url":null,"abstract":"<div><p>This work concerns with a class of chemotaxis models in which external sources, comprising nonlocal and gradient-dependent damping reactions, influence the motion of a cell density attracted by a chemical signal. The mechanism of the two densities is studied in bounded and impenetrable regions. In particular, it is seen that no gathering effect for the cells can appear in time provided that the damping impacts are sufficiently strong. Mathematically, we study this problem </p><div><div><span>$$ textstylebegin{cases} u_{t}=nabla cdot left ((u+1)^{m_{1}-1}nabla u -chi u(u+1)^{m_{2}-1} nabla vright )+ B(u,nabla u)&amp;{mathrm{in}} Omega times {t&gt;0} , tau v_{t}=Delta v-v+f(u) &amp;{mathrm{in}} Omega times {t&gt;0}, u_{nu }=v_{nu }=0 &amp;{mathrm{on}} partial Omega times {t&gt;0}, u(x, 0)=u_{0}(x), tau v(x,0)= tau v_{0}(x) &amp;x in bar{Omega }, end{cases} $$</span></div><div>\u0000 (◊)\u0000 </div></div><p> for </p><div><div><span>$$ B(u,nabla u)=B textrm{ being either ; } au^{alpha }-b u^{beta }-c int _{Omega }u^{delta }, textrm{ or ; } au^{alpha }-b u^{alpha }int _{Omega }u^{beta }-c|nabla u|^{delta }, $$</span></div></div><p> and where <span>(Omega )</span> is a bounded and smooth domain of <span>(mathbb{R}^{n})</span> (<span>(n in mathbb{N})</span>), <span>({t&gt;0}subseteq (0,infty ))</span> an open interval, <span>(tau in {0,1})</span>, <span>(m_{1},m_{2}in mathbb{R})</span>, <span>(chi ,a,b&gt;0)</span>, <span>(cgeq 0)</span>, and <span>(alpha , beta ,delta geq 1)</span>. Herein for <span>((x,t)in Omega times {t&gt;0})</span>, <span>(u=u(x,t))</span> stands for the population density, <span>(v=v(x,t))</span> for the chemical signal and <span>(f)</span> for a regular function describing the production law. The population density and the chemical signal are initially distributed accordingly to nonnegative and sufficiently regular functions <span>(u_{0}(x))</span> and <span>(tau v_{0}(x))</span>, respectively. For each of the expressions of <span>(B)</span>, sufficient conditions on parameters of the models ensuring that any nonnegative classical solution <span>((u,v))</span> to system (◊) is such that <span>({t&gt;0} equiv (0,infty ))</span> and uniformly bounded in time, are established. In the literature, most of the results concerning chemotaxis models with external sources deal with classical logistics, for which <span>(B=a u^{alpha }-b u^{beta })</span>. Thereafter, the introduction of dissipative effects as those expressed in <span>(B)</span> is the main novelty of this investigation. On the other hand, this paper extends the analyses in (Chiyo et al. in Appl. Math. Optim. 89(9):1–21, 2024; Bian et al. in Nonlinear Anal. 176:178–191, 2018; Latos in Nonlocal reaction preventing blow-up in the supercritical case of chemotaxis, 2020, arXiv:2011.10764).</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"195 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-025-00714-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143388883","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}

{"title":"Existence and Uniqueness Results for Generalized Non-local Hallaire-Luikov Moisture Transfer Equation","authors":"Asim Ilyas,&nbsp;Salman A. Malik,&nbsp;Kamran Suhaib","doi":"10.1007/s10440-025-00712-2","DOIUrl":"10.1007/s10440-025-00712-2","url":null,"abstract":"<div><p>This article focuses on inverse problem for Hallaire-Luikov moisture transfer equation involving Hilfer fractional derivative in time. Hallaire-Luikov equation is used to study heat and mass transfer in capillary-porous bodies. Spectral expansion method is used to find the solution of the inverse problem. By imposing certain conditions on the functions involved and utilizing certain properties of multinomial Mittag-Leffler function, it is shown that the solution to the equation, known as the inverse problem, is regular and unique. Moreover, the inverse problem exhibits ill-posedness in the sense of Hadamard. The article ends with an example to demonstrate these theoretical findings.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"195 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-025-00712-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143184605","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}

{"title":"The Effects of Diffusion Coefficients in a Two-Species Lotka-Volterra Competition System with Resource Dependent Dispersal","authors":"Qi Wang","doi":"10.1007/s10440-025-00715-z","DOIUrl":"10.1007/s10440-025-00715-z","url":null,"abstract":"<div><p>In this paper, we consider a Lotka-Volterra competition-diffusion system with resource-dependent dispersal. We study the linear v.s. global asymptotic stability of steady states. Furthermore, how the diffusion coefficients and the dispersal strategies of two competing species affect the stability of steady states are given. This paper is a further study of (Tang and Wang in J. Math. Biol. 86:23, 2023).</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"195 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143108252","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}

{"title":"Nonlocal Symmetries of Geng-Wu’s Super KdV Equation","authors":"Kai Tian,&nbsp;Hanyu Zhou,&nbsp;Cuiling Dong","doi":"10.1007/s10440-025-00709-x","DOIUrl":"10.1007/s10440-025-00709-x","url":null,"abstract":"<div><p>For a super Korteweg-de Vries (KdV) equation introduced by Geng and Wu, nonlocal infinitesimal symmetries depending on eigenfunctions of its (adjoint) linear spectral problem are constructed from gradient of the spectral parameter, and one of such symmetries is shown to be related to a nonlocal infinitesimal symmetry of Kupershmidt’s super modified KdV equation via a Miura-type transformation. On this basis, a finite symmetry transformation is established for an enlarged system, and leads to a non-trivial exact solution and a Bäcklund transformation of Geng-Wu’s super KdV equation. A procedure is explained to generate infinitely many conservation laws. Moreover, these results could be reduced to classical situations, and their bosonic limits are briefly summarized.</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":"143110180","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}

{"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}

{"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}

{"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}

{"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}

{"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}

{"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}