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Remarks on the Anisotropic Liouville Theorem for the Stationary Tropical Climate Model 关于固定热带气候模式的各向异性柳维尔定理的评论
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-10-17 DOI: 10.1007/s10440-024-00691-w
Huiting Ding, Fan Wu
{"title":"Remarks on the Anisotropic Liouville Theorem for the Stationary Tropical Climate Model","authors":"Huiting Ding,&nbsp;Fan Wu","doi":"10.1007/s10440-024-00691-w","DOIUrl":"10.1007/s10440-024-00691-w","url":null,"abstract":"<div><p>This paper studies the Liouville type theorems for stationary the tropical climate model on the whole space <span>(mathbb{R}^{3})</span>. It shows that if <span>((u,v,theta ))</span> satisfies certain anisotropic integrability conditions on the components of the <span>(u)</span> or <span>((u,v))</span>, also <span>(theta )</span> satisfies certain isotropic integrability conditions, there is only a trivial solution to the stationary tropical climate model. The results are a further extension of the recent work by Chae (Appl. Math. Lett. 142:108655, 2023).</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"194 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142447367","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
Asymptotic Study of a Singular Time-Dependent Brinkman Flow with Application 奇异时变布林克曼流的渐近研究及应用
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-10-17 DOI: 10.1007/s10440-024-00689-4
Fatma Boumiza, Jamel Ferchichi, Houcine Meftahi
{"title":"Asymptotic Study of a Singular Time-Dependent Brinkman Flow with Application","authors":"Fatma Boumiza,&nbsp;Jamel Ferchichi,&nbsp;Houcine Meftahi","doi":"10.1007/s10440-024-00689-4","DOIUrl":"10.1007/s10440-024-00689-4","url":null,"abstract":"<div><p>In this article we address the problem of locating point forces within a time-dependent singular Brinkman flow. The context of the study is framed as an approximation of cerebrospinal fluid (CSF) around the central nervous system, with the point forces representing a model for the blood-brain barrier. We approach the problem by reformulating the identification task as an optimization problem, employing a tracking shape functional. A notable challenge in this study arises from the irregularity in the solution of the partial differential equation (PDE), which complicates the exploration of sensitivity analysis. To overcome this issue, we employ a relaxation method and compute the topological derivative of the cost function. The topological derivative, commonly used in shape optimization problems, offers insights into how the cost function responds to small perturbations in the domain. To determine the optimal position of the point forces, we employ a one-shot algorithm based on the derived topological gradient. Finally, we present numerical results that showcase the efficiency of our method in addressing the identified problem.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"194 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142443355","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
Characterization of Initial Layer for Fast Chemical Diffusion Limit in Keller-Segel System 凯勒-西格尔系统中快速化学扩散极限的初始层特征
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-10-16 DOI: 10.1007/s10440-024-00695-6
Min Li, Zhaoyin Xiang
{"title":"Characterization of Initial Layer for Fast Chemical Diffusion Limit in Keller-Segel System","authors":"Min Li,&nbsp;Zhaoyin Xiang","doi":"10.1007/s10440-024-00695-6","DOIUrl":"10.1007/s10440-024-00695-6","url":null,"abstract":"<div><p>This paper investigates the fast chemical diffusion limit from a parabolic-parabolic Keller-Segel system to the corresponding parabolic-elliptic Keller-Segel system by constructing approximate solutions with an appropriate order via an asymptotic expansion. Nonlinear stability of the precise initial layer is characterized with an exact convergence rate by using basic energy method.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"194 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142438874","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
Asymptotically Linear Euclidean Bosonic Equations 近似线性欧几里得玻色方程
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-10-15 DOI: 10.1007/s10440-024-00693-8
Cuicui Long, Jinggang Tan, Aliang Xia
{"title":"Asymptotically Linear Euclidean Bosonic Equations","authors":"Cuicui Long,&nbsp;Jinggang Tan,&nbsp;Aliang Xia","doi":"10.1007/s10440-024-00693-8","DOIUrl":"10.1007/s10440-024-00693-8","url":null,"abstract":"<div><p>We investigate the following nonlinear bosonic equation on Euclidean space arising in string theory and cosmology: </p><div><div><span>$$ -Delta e^{-cDelta }u+mu=f(x,u),quad xin {mathbb{R}}^{n}, $$</span></div><div>\u0000 (P)\u0000 </div></div><p> where <span>(nge 3)</span>, <span>(m&gt;0)</span>, <span>(c&gt;0)</span> and <span>(frac{f(x,u)}{u})</span> tends to a positive function <span>(h(x))</span> independent of <span>(u)</span> as <span>(urightarrow +infty )</span>, <span>(e^{-cDelta })</span> is given by a power series with <span>(Delta )</span> is the Euclidean Laplace operator. Here, the nonlinear term <span>(f(x,u))</span> does not satisfy the usual condition: </p><div><div><span>$$ 0le F(x,u):=int _{0}^{u}f(x,t),dtle frac{1}{2+theta }f(x,u)u, $$</span></div><div>\u0000 (AR)\u0000 </div></div><p> for <span>(theta &gt;0)</span> and <span>(|u|)</span> is large, which is important in using the mountain pass theorem, see Alves et al. (J. Differ. Equ. 323:229-252, 2022) and Corrêa et al. (J. Differ. Equ. 363:491-517, 2023). This paper is devoted to discuss how to use the mountain pass theorem to obtain the existence of nontrivial solution to problem (P) without the (AR) condition.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"193 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142438848","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
Unveiling the Interplay Between Degree-Based Graph Invariants of a Graph and Its Random Subgraphs 揭示基于度的图不变式与随机子图之间的相互作用
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-10-14 DOI: 10.1007/s10440-024-00688-5
Mohammad Ali Hosseinzadeh
{"title":"Unveiling the Interplay Between Degree-Based Graph Invariants of a Graph and Its Random Subgraphs","authors":"Mohammad Ali Hosseinzadeh","doi":"10.1007/s10440-024-00688-5","DOIUrl":"10.1007/s10440-024-00688-5","url":null,"abstract":"<div><p>This paper investigates the significance of employing random subgraphs and analyzing the expected values of Zagreb ndices within chemical graphs. By examining smaller, representative subsets, we uncover valuable insights into the properties and characteristics of complex networks. The expected values of Zagreb indices serve as critical mathematical measures for quantifying the structural complexity of chemical graphs, providing essential information about connectivity and branching patterns within molecules. Our primary contribution includes deriving theoretical expressions for these indices and validating them through extensive computational experiments on fullerene graphs <span>(C_{20})</span> and <span>(C_{60})</span>. The results demonstrate that our theoretical predictions closely align with experimental findings, affirming the robustness of Zagreb indices in characterizing molecular structures. Additionally, our analysis of specific cases, such as complete graphs and complete bipartite graphs, is consistent with previous studies, further reinforcing our methodology. This research emphasizes the relevance of random subgraphs and expected values of Zagreb indices in advancing our understanding of molecular behavior and stability, with important implications for materials science and drug design.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"193 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142434802","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 Bounded Solutions and Large Time Behavior of a Chemotaxis System with Flux Limitation 具有通量限制的趋化系统的全局有界解法和大时间行为
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-10-10 DOI: 10.1007/s10440-024-00690-x
Chun Wu
{"title":"Global Bounded Solutions and Large Time Behavior of a Chemotaxis System with Flux Limitation","authors":"Chun Wu","doi":"10.1007/s10440-024-00690-x","DOIUrl":"10.1007/s10440-024-00690-x","url":null,"abstract":"<div><p>In this paper, the following cross-diffusion system is investigated </p><div><div><span>$$ textstylebegin{cases} u_{t}=nabla cdot big((u+1)^{m}nabla ubig)-nabla cdot Bigg( frac{u(u+1)^{beta -1}nabla v}{(1+|nabla v|^{2})^{alpha }}Bigg)+a-bu^{r}, ,,&amp; xin Omega ,,,t&gt;0, 0=Delta v-v+u, &amp; xin Omega ,,,t&gt;0, end{cases} $$</span></div></div><p> in a bounded domain <span>(Omega subset mathbb{R}^{n})</span> (<span>(nge 2)</span>) with smooth boundary <span>(partial Omega )</span>. Under the condition that <span>(alpha &gt;frac{2n-mn-2}{2(n-1)})</span>, <span>(mgeq 1)</span>, and <span>(beta leq frac{m+2}{2})</span>, it is shown that the problem possesses a unique global bounded classical solution. Moreover, it is obtained that the corresponding solution exponentially converge to a constant stationary solution when the initial data <span>(u_{0})</span> is sufficiently small.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"193 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00690-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142411173","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
Pseudorandomness of the Schrödinger Map Equation 薛定谔映射方程的伪随机性
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-10-07 DOI: 10.1007/s10440-024-00687-6
Sandeep Kumar
{"title":"Pseudorandomness of the Schrödinger Map Equation","authors":"Sandeep Kumar","doi":"10.1007/s10440-024-00687-6","DOIUrl":"10.1007/s10440-024-00687-6","url":null,"abstract":"<div><p>A unique behaviour of the Schrödinger map equation, a geometric partial differential equation, is presented by considering its evolution for regular polygonal curves in both Euclidean and hyperbolic spaces. The results are consistent with those for the vortex filament equation, an equivalent form of the Schrödinger map equation in the Euclidean space. Thus, with all possible choices of regular polygons in a given setting, our analysis not only provides a novel extension to its usefulness as a pseudorandom number generator but also complements the existing results.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"193 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00687-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142410454","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
Local Strong Solution for a Nonhomogeneous Incompressible Cell-Fluid Navier-Stokes Model with Chemotaxis 具有趋化性的非均质不可压缩细胞-流体纳维-斯托克斯模型的局部强解法
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-09-26 DOI: 10.1007/s10440-024-00685-8
Juliana Honda Lopes, Gabriela Planas
{"title":"Local Strong Solution for a Nonhomogeneous Incompressible Cell-Fluid Navier-Stokes Model with Chemotaxis","authors":"Juliana Honda Lopes,&nbsp;Gabriela Planas","doi":"10.1007/s10440-024-00685-8","DOIUrl":"10.1007/s10440-024-00685-8","url":null,"abstract":"<div><p>This paper addresses a general nonhomogeneous incompressible cell-fluid Navier-Stokes model incorporating chemotaxis in a two or three-dimensional bounded domain. This model comprises two mass balance equations and two general momentum balance equations, specifically for the cell and fluid phases, combined with a convection-diffusion-reaction equation for oxygen. We establish the existence and uniqueness of a local strong solution under initial data that satisfy natural compatibility conditions. Additionally, we present a blow-up criterion for the strong solution.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"193 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00685-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142414186","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
Partially Dissipative Viscous System of Balance Laws and Application to Kuznetsov–Westervelt Equation 部分耗散粘性平衡定律系统及其在库兹涅佐夫-韦斯特韦尔特方程中的应用
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-09-25 DOI: 10.1007/s10440-024-00686-7
Gilbert Peralta
{"title":"Partially Dissipative Viscous System of Balance Laws and Application to Kuznetsov–Westervelt Equation","authors":"Gilbert Peralta","doi":"10.1007/s10440-024-00686-7","DOIUrl":"10.1007/s10440-024-00686-7","url":null,"abstract":"<div><p>We provide the well-posedness for a partially dissipative viscous system of balance laws in smooth Sobolev spaces under the same assumptions as in the case of inviscid balance laws. A priori estimates for coupled hyperbolic-parabolic linear systems with coefficients having limited regularity are derived using Friedrichs regularization and Moser-type estimates. Local existence for nonlinear systems will be established using the results of the linear theory and a suitable iteration scheme. The local existence theory is then applied to the Kuznetsov–Westervelt equation with damping for nonlinear wave acoustic propagation. Existence of global solutions for small data and their asymptotic stability are established.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"193 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-09-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142413710","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 Nonlocal and Nonlinear System for Cell-Cell Communication 细胞间通信的非局部非线性系统分析
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-09-12 DOI: 10.1007/s10440-024-00676-9
Diego Chamorro, Nicolas Meunier
{"title":"Analysis of a Nonlocal and Nonlinear System for Cell-Cell Communication","authors":"Diego Chamorro,&nbsp;Nicolas Meunier","doi":"10.1007/s10440-024-00676-9","DOIUrl":"10.1007/s10440-024-00676-9","url":null,"abstract":"<div><p>We consider a system of two nonlocal and nonlinear partial differential equations that describe some aspects of yeast cell-cell communication. We study local and global existence and uniqueness of solutions. We consider mild solutions and we perform bilinear and trilinear fixed point arguments in suitable functional spaces.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"193 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218842","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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