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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
Stability of the Ionic Parameters of a Nonlocal FitzHugh-Nagumo Model of Cardiac Electrophysiology 心脏电生理学非局部 FitzHugh-Nagumo 模型离子参数的稳定性
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-09-09 DOI: 10.1007/s10440-024-00682-x
Narjess Ben Abid, Mostafa Bendahmane, Moncef Mahjoub
{"title":"Stability of the Ionic Parameters of a Nonlocal FitzHugh-Nagumo Model of Cardiac Electrophysiology","authors":"Narjess Ben Abid,&nbsp;Mostafa Bendahmane,&nbsp;Moncef Mahjoub","doi":"10.1007/s10440-024-00682-x","DOIUrl":"10.1007/s10440-024-00682-x","url":null,"abstract":"<div><p>This paper presents an inverse problem of identifying two ionic parameters of a nonlocal reaction-diffusion system in cardiac electrophysiology modelling. We used a nonlocal FitzHugh-Nagumo monodomain model which describes the electrical activity in cardiac tissue with the diffusion rate assumed to depend on the total electrical potential in the heart. We established at first, the global Carleman estimate adapted to nonlocal diffusion to obtain our main result which is the uniqueness and the Lipschitz stability estimate for two ionic parameters <span>((k,gamma ))</span>.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"193 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218863","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
Ultimate Boundedness of a Stochastic Chemostat Model with Periodic Nutrient Input and Random Disturbance 具有周期性营养输入和随机扰动的随机恒温模型的终极约束性
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-09-09 DOI: 10.1007/s10440-024-00683-w
Xiaofeng Zhang, Yujing Zhang
{"title":"Ultimate Boundedness of a Stochastic Chemostat Model with Periodic Nutrient Input and Random Disturbance","authors":"Xiaofeng Zhang,&nbsp;Yujing Zhang","doi":"10.1007/s10440-024-00683-w","DOIUrl":"10.1007/s10440-024-00683-w","url":null,"abstract":"<div><p>Stochastic ultimate boundedness has always been a very important property, which plays an important role in the study of stochastic models. Thus, in this paper, we will study a stochastic periodic chemostat system, in which we assume that the nutrient input concentration and noise intensities are periodic. In order to make the stochastic periodic model have mathematical and biological significance, we will study a very important issue: the existence, uniqueness and ultimate boundedness of a global positive solution for a stochastic periodic chemostat system.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"193 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218864","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
Wong-Zakai Approximations for the Stochastic Landau-Lifshitz-Bloch Equation with Helicity 带螺旋性的随机朗道-利夫希茨-布洛赫方程的黄扎凯近似值
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-09-03 DOI: 10.1007/s10440-024-00681-y
Soham Sanjay Gokhale
{"title":"Wong-Zakai Approximations for the Stochastic Landau-Lifshitz-Bloch Equation with Helicity","authors":"Soham Sanjay Gokhale","doi":"10.1007/s10440-024-00681-y","DOIUrl":"10.1007/s10440-024-00681-y","url":null,"abstract":"<div><p>For temperatures below and beyond the Curie temperature, the stochastic Landau-Lifshitz-Bloch equation describes the evolution of spins in ferromagnetic materials. In this work, we consider the stochastic Landau-Lifshitz-Bloch equation driven by a real valued Wiener process and show Wong-Zakai type approximations for the same. We consider non-zero contribution from the helicity term in the energy. First, using a Doss-Sussmann type transform, we convert the stochastic partial differential equation into a deterministic equation with random coefficients. We then show that the solution of the transformed equation depends continuously on the driving Wiener process. We then use this result, along with the properties of the said transform to show that the solution of the originally considered equation depends continuously on the driving Wiener process.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"193 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218865","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
Approximations of 2D and 3D Stochastic Convective Brinkman-Forchheimer Extended Darcy Equations 二维和三维随机对流布林克曼-福克海默扩展达西方程的近似值
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-08-28 DOI: 10.1007/s10440-024-00680-z
Manil T. Mohan
{"title":"Approximations of 2D and 3D Stochastic Convective Brinkman-Forchheimer Extended Darcy Equations","authors":"Manil T. Mohan","doi":"10.1007/s10440-024-00680-z","DOIUrl":"10.1007/s10440-024-00680-z","url":null,"abstract":"<div><p>In this article, we consider two- and three- dimensional stochastic convective Brinkman-Forchheimer extended Darcy (CBFeD) equations </p><div><div><span>$$ frac{partial boldsymbol{u}}{partial t}-mu Delta boldsymbol{u}+( boldsymbol{u}cdot nabla )boldsymbol{u}+alpha |boldsymbol{u}|^{q-1} boldsymbol{u}+beta |boldsymbol{u}|^{r-1}boldsymbol{u}+nabla p= boldsymbol{f}, nabla cdot boldsymbol{u}=0, $$</span></div></div><p> on a torus, where <span>(mu ,beta &gt;0)</span>, <span>(alpha in mathbb{R})</span>, <span>(rin [1,infty ))</span> and <span>(qin [1,r))</span>. The goal is to show that the solutions of 2D and 3D stochastic CBFeD equations driven by Brownian motion can be approximated by 2D and 3D stochastic CBFeD equations forced by pure jump noise/random kicks on the state space <span>(mathrm{D}([0,T];mathbb{H}))</span>. For the cases <span>(d=2)</span>, <span>(rin [1,infty ))</span> and <span>(d=3)</span>, <span>(rin (3,infty ))</span>, by using minimal regularity assumptions on the noise coefficient, the results are established for any <span>(mu ,beta &gt;0)</span>. For the case <span>(d=r=3)</span>, the same results are obtained for <span>(2beta mu geq 1)</span>.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"193 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218866","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 Regularity of Positive Solutions for Schrödinger-Maxwell System with Singularity 具有奇异性的薛定谔-麦克斯韦系统正解的存在性和规律性
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-08-22 DOI: 10.1007/s10440-024-00679-6
Abdelaaziz Sbai, Youssef El Hadfi, Mounim El Ouardy
{"title":"Existence and Regularity of Positive Solutions for Schrödinger-Maxwell System with Singularity","authors":"Abdelaaziz Sbai,&nbsp;Youssef El Hadfi,&nbsp;Mounim El Ouardy","doi":"10.1007/s10440-024-00679-6","DOIUrl":"10.1007/s10440-024-00679-6","url":null,"abstract":"<div><p>In this paper we study the existence of positive solutions for the following Schrödinger–Maxwell system of singular elliptic equations </p><div><div><span>$$ textstylebegin{cases} -operatorname{div}(A(x) nabla u)+psi u^{r-1}= frac{f(x)}{u^{theta }} &amp; text{ in } Omega , -operatorname{div}(M(x) psi )=u^{r} &amp; text{ in } Omega , u, psi &gt;0 &amp; text{ in } Omega , u=psi =0 &amp; text{ on } partial Omega ,end{cases} $$</span></div><div>\u0000 (1)\u0000 </div></div><p> where <span>(Omega )</span> is a bounded open set of <span>(mathbb{R}^{N}, N&gt;2)</span>, <span>(r&gt;1)</span>, <span>(0 &lt; theta &lt;1)</span> and <span>(f)</span> is nonnegative function belongs to a suitable Lebesgue space. In particular, we take advantage of the coupling between the two equations of the system by proving how the structure of the system gives rise to a regularizing effect on the summability of the solutions.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"193 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218867","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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