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Global Classical Solutions to a Predator-Prey Model with Nonlinear Indirect Chemotaxis Mechanism 具有非线性间接趋化机制的捕食者-猎物模型的全局经典解法
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-04-10 DOI: 10.1007/s10440-024-00648-z
Chang-Jian Wang, Chun-Hai Ke
{"title":"Global Classical Solutions to a Predator-Prey Model with Nonlinear Indirect Chemotaxis Mechanism","authors":"Chang-Jian Wang,&nbsp;Chun-Hai Ke","doi":"10.1007/s10440-024-00648-z","DOIUrl":"10.1007/s10440-024-00648-z","url":null,"abstract":"<div><p>We deal with the following predator-prey model involving nonlinear indirect chemotaxis mechanism </p><div><div><span>$$ left { textstylebegin{array}{l@{quad }l} u_{t}=Delta u+xi nabla cdot (u nabla w)+a_{1}u(1-u^{r_{1}-1}-b_{1}v), &amp; xin Omega , t&gt;0, v_{t}=Delta v-chi nabla cdot (v nabla w)+a_{2}v(1-v^{r_{2}-1}+b_{2}u), &amp; xin Omega , t&gt;0, w_{t}=Delta w-w+z^{gamma }, &amp; xin Omega , t&gt;0, 0=Delta z-z+u^{alpha }+v^{beta }, &amp; xin Omega , t&gt;0 , end{array}displaystyle right . $$</span></div></div><p> under homogeneous Neumann boundary conditions in a bounded and smooth domain <span>(Omega subset mathbb{R}^{n})</span> (<span>(ngeq 1)</span>), where the parameters <span>(xi ,chi ,a_{1},a_{2},b_{1},b_{2},alpha ,beta ,gamma &gt;0)</span>. It has been shown that if <span>(r_{1}&gt;1)</span>, <span>(r_{2}&gt;2)</span> and <span>(gamma (alpha +beta )&lt;frac{2}{n})</span>, then there exist some suitable initial data such that the system has a global classical solution <span>((u,v,w,z))</span>, which is bounded in <span>(Omega times (0,infty ))</span>. Compared to the previous contributions, in this work, the boundedness criteria are only determined by the power exponents <span>(r_{1})</span>, <span>(r_{2})</span>, <span>(alpha )</span>, <span>(beta )</span>, <span>(gamma )</span> and spatial dimension <span>(n)</span> instead of the coefficients of the system and the sizes of initial data.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00648-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140591841","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
Efficient Numerical Schemes for a Two-Species Keller-Segel Model and Investigation of Its Blowup Phenomena in 3D 双物种凯勒-西格尔模型的高效数值方案及其三维爆破现象研究
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-04-10 DOI: 10.1007/s10440-024-00647-0
Xueling Huang, Jie Shen
{"title":"Efficient Numerical Schemes for a Two-Species Keller-Segel Model and Investigation of Its Blowup Phenomena in 3D","authors":"Xueling Huang,&nbsp;Jie Shen","doi":"10.1007/s10440-024-00647-0","DOIUrl":"10.1007/s10440-024-00647-0","url":null,"abstract":"<div><p>We consider in this paper numerical approximation and simulation of a two-species Keller-Segel model. The model enjoys an energy dissipation law, mass conservation and bound or positivity preserving for the population density of two species. We construct a class of very efficient numerical schemes based on the generalized scalar auxiliary variable with relaxation which preserve unconditionally the essential properties of the model at the discrete level. We conduct a sequence of numerical tests to validate the properties of these schemes, and to study the blow-up phenomena of the model in a three-dimensional domain in parabolic-elliptic form and parabolic-parabolic form.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00647-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140591845","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
A New Blowup Criterion to the Cauchy Problem for the Three-Dimensional Compressible Viscous Micropolar Fluids with Vacuum 带真空的三维可压缩粘性微极性流体考奇问题的新吹胀准则
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-04-04 DOI: 10.1007/s10440-024-00642-5
Xiaofeng Hou, Yinjie Xu
{"title":"A New Blowup Criterion to the Cauchy Problem for the Three-Dimensional Compressible Viscous Micropolar Fluids with Vacuum","authors":"Xiaofeng Hou,&nbsp;Yinjie Xu","doi":"10.1007/s10440-024-00642-5","DOIUrl":"10.1007/s10440-024-00642-5","url":null,"abstract":"<div><p>In this paper, we prove a new blowup criterion for the strong solution to the Cauchy problem of three-dimensional micropolar fluid equation with vacuum. Specifically, we establish a blowup criterion in terms of <span>(L_{t}^{infty }L_{x}^{q})</span> of the density, where <span>(1&lt; q&lt;infty )</span>, and it is independent on the velocity of rotation of the microscopic particles.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140591546","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 Tension Spline Based Numerical Algorithm for Singularly Perturbed Partial Differential Equations on Non-uniform Discretization 基于张力样条的非均匀离散奇异扰动偏微分方程数值算法
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-04-03 DOI: 10.1007/s10440-024-00645-2
Murali Mohan Kumar P., Ravi Kanth A.S.V.
{"title":"A Tension Spline Based Numerical Algorithm for Singularly Perturbed Partial Differential Equations on Non-uniform Discretization","authors":"Murali Mohan Kumar P.,&nbsp;Ravi Kanth A.S.V.","doi":"10.1007/s10440-024-00645-2","DOIUrl":"10.1007/s10440-024-00645-2","url":null,"abstract":"<div><p>The present study investigates an algorithm numerically for finding the solution of partial differential equation with differences involved singular perturbation parameter(SPPDE) on non-uniform grid. Taylor series expansion provides a close approximation of the delay and advance terms in the convection-diffusion terms. After the approximations in shift containing terms, we applied the Crank-Nicolson application on uniform grid in the vertical direction. Subsequently, the resultant system is employed by the method of tension spline on a piece-wise uniform grid. Empirical evidence has shown that the suggested approach exhibits second-order characteristics in both the spatial and temporal dimensions. The effectiveness of derived scheme demonstrated through the solution of examples and the results are compared with existed methods. In the conclusion section, we will discuss the effect of shift parameters behavior for various singular perturbation parameter.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140591705","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
Threshold Dynamics for Diffusive Age-Structured Model over Unbounded Domains: Age-Dependent Death and Diffusion Rates 无界域上扩散年龄结构模型的阈值动力学：依赖年龄的死亡和扩散率
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-03-28 DOI: 10.1007/s10440-024-00643-4
Mohammadkheer AlJararha
{"title":"Threshold Dynamics for Diffusive Age-Structured Model over Unbounded Domains: Age-Dependent Death and Diffusion Rates","authors":"Mohammadkheer AlJararha","doi":"10.1007/s10440-024-00643-4","DOIUrl":"10.1007/s10440-024-00643-4","url":null,"abstract":"<div><p>The global dynamics of the typical age-structured model with age-dependent mortality and diffusion rates on unbounded domains have been established. On the one hand, we showed that a positive and constant state solution of the mature population is globally asymptotically stable with respect to the compact-open topology; on the other hand, we showed that the trivial solution is globally asymptotically stable with respect to the usual supremum norm. As an application of our result, we applied the result to birth functions appearing in biology. In addition to the theoretical results, we also present a numerical simulation.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140325843","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 Error Bounds for the Extended Vertical Linear Complementarity Problems of CKV-Type Matrices and CKV-Type (B)-Matrices CKV 型矩阵和 CKV 型 $B$ - 矩阵的扩展垂直线性互补问题的全局误差约束
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-03-28 DOI: 10.1007/s10440-024-00644-3
Lei Gao, Xiudan Jia, Xia Jing, Yi Liu
{"title":"Global Error Bounds for the Extended Vertical Linear Complementarity Problems of CKV-Type Matrices and CKV-Type (B)-Matrices","authors":"Lei Gao,&nbsp;Xiudan Jia,&nbsp;Xia Jing,&nbsp;Yi Liu","doi":"10.1007/s10440-024-00644-3","DOIUrl":"10.1007/s10440-024-00644-3","url":null,"abstract":"<div><p>Some global error bounds with undetermined parameters, which are not always valid, for the extended vertical linear complementarity problems (LCP) of CKV-type matrices and CKV-type <span>(B)</span>-matrices, are presented by Yan and Wang (Jpn. J. Ind. Appl. Math. 41:129–150, 2024). In this paper, new global error bounds for the extended vertical LCP of CKV-type matrices and CKV-type <span>(B)</span>-matrices are given, which depend only on the entries of the involved matrices. Numerical examples show that the new bounds are better than those provided in Zhang et al. (Comput. Optim. Appl. 42(3):335–352, 2009) and Wang et al. (Comput. Appl. Math. 40:148, 2021) in some cases.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140325685","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
An Attraction-Repulsion Chemotaxis System: The Roles of Nonlinear Diffusion and Productions 吸引-推进趋化系统：非线性扩散和生产的作用
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-03-13 DOI: 10.1007/s10440-024-00641-6
Zhan Jiao, Irena Jadlovská, Tongxing Li
{"title":"An Attraction-Repulsion Chemotaxis System: The Roles of Nonlinear Diffusion and Productions","authors":"Zhan Jiao,&nbsp;Irena Jadlovská,&nbsp;Tongxing Li","doi":"10.1007/s10440-024-00641-6","DOIUrl":"10.1007/s10440-024-00641-6","url":null,"abstract":"<div><p>This article considers the no-flux attraction-repulsion chemotaxis model </p><div><div><span>$$ left { textstylebegin{array}{l} begin{aligned} &amp;u_{t} = nabla cdot big((u+1)^{m_{1}-1}nabla u-chi u(u+1)^{m_{2}-2} nabla v+xi u(u+1)^{m_{3}-2}nabla wbig),&amp; xin Omega , t&gt;0&amp;, &amp; 0=Delta v+f(u)-beta v, &amp; xin Omega , t&gt;0&amp;, &amp; 0=Delta w+g(u)-delta w, &amp; xin Omega , t&gt;0&amp; end{aligned} end{array}displaystyle right . $$</span></div></div><p> defined in a smooth and bounded domain <span>(Omega subset mathbb{R}^{n})</span> (<span>(nge 2)</span>) with <span>(m_{1},m_{2},m_{3}in mathbb{R})</span>, <span>(chi ,xi ,beta ,delta &gt;0)</span>. The functions <span>(f(u))</span>, <span>(g(u))</span> extend the prototypes <span>(f(u)=alpha u^{s})</span> and <span>(g(u)=gamma u^{r})</span> with <span>(alpha ,gamma &gt;0)</span> and suitable <span>(s,r&gt;0)</span> for all <span>(uge 0)</span>. Our main result exhibits that there exists <span>(M^{*}&gt;0)</span> such that for all properly regular initial data, the studied model admits a unique classical solution which remains bounded if <span>(m_{2}+s&lt; m_{3}+r)</span> or <span>(m_{2}+s=m_{3}+r)</span> and <span>(frac{xi gamma }{chi alpha }&gt;M^{*})</span>.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140128943","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 and Localization of Unbounded Solutions for Fully Nonlinear Systems of Jerk Equations on the Half-Line 半线上全非线性跃迁方程系统的无界解的存在性与定位
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-03-13 DOI: 10.1007/s10440-024-00635-4
Ali Zerki, Kamal Bachouche, Karima Ait-Mahiout
{"title":"Existence and Localization of Unbounded Solutions for Fully Nonlinear Systems of Jerk Equations on the Half-Line","authors":"Ali Zerki,&nbsp;Kamal Bachouche,&nbsp;Karima Ait-Mahiout","doi":"10.1007/s10440-024-00635-4","DOIUrl":"10.1007/s10440-024-00635-4","url":null,"abstract":"<div><p>In the following paper, we have shown the existence and localization of solutions for a system of <span>(n)</span> third order differential equations under Sturm-Liouville type boundary conditions. Such systems appear in many physical problems, one of which is the jerk equations to locate the trajectory of a material point in space.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140128945","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
Uniform Turnpike Property and Singular Limits 统一岔道属性和奇异极限
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-03-07 DOI: 10.1007/s10440-024-00640-7
Martín Hernández, Enrique Zuazua
{"title":"Uniform Turnpike Property and Singular Limits","authors":"Martín Hernández,&nbsp;Enrique Zuazua","doi":"10.1007/s10440-024-00640-7","DOIUrl":"10.1007/s10440-024-00640-7","url":null,"abstract":"<div><p>Motivated by singular limits for long-time optimal control problems, we investigate a class of parameter-dependent parabolic equations. First, we prove a turnpike result, uniform with respect to the parameters within a suitable regularity class and under appropriate bounds. The main ingredient of our proof is the justification of the uniform exponential stabilization of the corresponding Riccati equations, which is derived from the uniform null control properties of the model.</p><p>Then, we focus on a heat equation with rapidly oscillating coefficients. In the one-dimensional setting, we obtain a uniform turnpike property with respect to the highly oscillatory heterogeneous medium. Afterward, we establish the homogenization of the turnpike property. Finally, our results are validated by numerical experiments.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00640-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140055639","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
Swarm-Based Optimization with Random Descent 基于随机后裔的蜂群优化
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-03-01 DOI: 10.1007/s10440-024-00639-0
Eitan Tadmor, Anil Zenginoğlu
{"title":"Swarm-Based Optimization with Random Descent","authors":"Eitan Tadmor,&nbsp;Anil Zenginoğlu","doi":"10.1007/s10440-024-00639-0","DOIUrl":"10.1007/s10440-024-00639-0","url":null,"abstract":"<div><p>We extend our study of the swarm-based gradient descent method for non-convex optimization, (Lu et al., Swarm-based gradient descent method for non-convex optimization, 2022, arXiv:2211.17157), to allow random descent directions. We recall that the swarm-based approach consists of a swarm of agents, each identified with a position, <span>(mathbf{x})</span>, and mass, <span>(m)</span>. The key is the transfer of mass from high ground to low(-est) ground. The mass of an agent dictates its step size: lighter agents take larger steps. In this paper, the essential new feature is the choice of direction: rather than restricting the swarm to march in the steepest gradient descent, we let agents proceed in randomly chosen directions centered around — but otherwise different from — the gradient direction. The random search secures the descent property while at the same time, enabling greater exploration of ambient space. Convergence analysis and benchmark optimizations demonstrate the effectiveness of the swarm-based random descent method as a multi-dimensional global optimizer.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"190 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140019920","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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