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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
An Alternated Inertial Projection and Contraction Algorithm for Solving Quasimonotone Bilevel Variational Inequalities with Application to Optimal Control Problems 一种用于求解准多项式双级变分不等式的交替惯性投影和收缩算法，并将其应用于最优控制问题
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-08-21 DOI: 10.1007/s10440-024-00678-7
O. T. Mewomo, V. A. Uzor, A. Gibali
{"title":"An Alternated Inertial Projection and Contraction Algorithm for Solving Quasimonotone Bilevel Variational Inequalities with Application to Optimal Control Problems","authors":"O. T. Mewomo,&nbsp;V. A. Uzor,&nbsp;A. Gibali","doi":"10.1007/s10440-024-00678-7","DOIUrl":"10.1007/s10440-024-00678-7","url":null,"abstract":"<div><p>We are focused on solving a general class of bilevel variational inequalities involving quasimonotone operators in real Hilbert spaces. A strong convergent iterative method for solving the problem is presented and analysed. Our work generalizes several existing results in the literature and holds two major mathematical advantages. 1) Any generated sequence by the algorithm preserves the Fejér monotonicity property; and 2) There is no need to execute a line-search or know a-prior the strongly monotone coefficient or Lipschitz constant. Numerical experiments with comparisons to existing/related methods illustrate the performances of the proposed method and in particular, application to optimal control problems suggests the practical potential of our scheme.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"193 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142218869","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
Limiting Behavior of Nonlocal Stochastic Schrödinger Lattice Systems with Time-Varying Delays in Weighted Space 加权空间中具有时变延迟的非局部随机薛定谔晶格系统的极限行为
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-08-08 DOI: 10.1007/s10440-024-00677-8
Xintao Li, Lianbing She
{"title":"Limiting Behavior of Nonlocal Stochastic Schrödinger Lattice Systems with Time-Varying Delays in Weighted Space","authors":"Xintao Li,&nbsp;Lianbing She","doi":"10.1007/s10440-024-00677-8","DOIUrl":"10.1007/s10440-024-00677-8","url":null,"abstract":"<div><p>This paper deals with the limiting behavior of nonlocal stochastic Schrödinger lattice systems with time-varying delays and multiplicative noise in weighted space. We first consider the existence and uniqueness of tempered pullback random attractors for considered stochastic system and then establish the upper-semicontinuity of these attractors when the length of time delay approaches zero.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"192 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00677-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941159","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
On Augmented Dimensional Analysis 关于增量维度分析
IF 1.2 4区 数学
Acta Applicandae Mathematicae Pub Date : 2024-08-05 DOI: 10.1007/s10440-024-00673-y
Dan Jonsson
{"title":"On Augmented Dimensional Analysis","authors":"Dan Jonsson","doi":"10.1007/s10440-024-00673-y","DOIUrl":"10.1007/s10440-024-00673-y","url":null,"abstract":"<div><p>We present an innovative approach to dimensional analysis, referred to as augmented dimensional analysis and based on a representation theorem for complete quantity functions with a scaling-covariant scalar representation. This new theorem, grounded in a purely algebraic theory of quantity spaces, allows the classical <span>(pi )</span> theorem to be restated in an explicit and precise form and its prerequisites to be clarified and relaxed. Augmented dimensional analysis, in contrast to classical dimensional analysis, is guaranteed to take into account all relations among the quantities involved. Several examples are given to show that the information thus gained, together with symmetry assumptions, can lead to new or stronger results. We also explore the connection between dimensional analysis and matroid theory, elucidating combinatorial aspects of dimensional analysis. It is emphasized that dimensional analysis rests on a principle of covariance.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"192 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-024-00673-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141941160","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
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