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Stability for an Interface Transmission Problem of Wave-Plate Equations with Dynamical Boundary Controls 具有动态边界控制的波片方程界面传输问题的稳定性
IF 1.6 4区 数学
Acta Applicandae Mathematicae Pub Date : 2023-11-22 DOI: 10.1007/s10440-023-00611-4
Zahraa Abdallah, Stéphane Gerbi, Chiraz Kassem, Ali Wehbe
{"title":"Stability for an Interface Transmission Problem of Wave-Plate Equations with Dynamical Boundary Controls","authors":"Zahraa Abdallah,&nbsp;Stéphane Gerbi,&nbsp;Chiraz Kassem,&nbsp;Ali Wehbe","doi":"10.1007/s10440-023-00611-4","DOIUrl":"10.1007/s10440-023-00611-4","url":null,"abstract":"<div><p>We investigate a two-dimensional transmission model consisting of a wave equation and a Kirchhoff plate equation with dynamical boundary controls under geometric conditions. The two equations are coupled through transmission conditions along a steady interface between the domains in which the wave and plate equations evolve, respectively. Our primary concern is the stability analysis of the system, which has not appeared in the literature. For this aim, using a unique continuation theorem, the strong stability of the system is proved without any geometric condition and in the absence of compactness of the resolvent. Then, we show that our system lacks exponential (uniform) stability. However, we establish a polynomial energy decay estimate of type <span>(1/t)</span> for smooth initial data using the frequency domain approach from semigroup theory, which combines a contradiction argument with the multiplier technique. This method leads to certain geometrical conditions concerning the wave’s and the plate’s domains.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"188 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-11-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138431671","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
Incompressible Limits of the Patlak-Keller-Segel Model and Its Stationary State patak - keller - segel模型的不可压缩极限及其定态
IF 1.6 4区 数学
Acta Applicandae Mathematicae Pub Date : 2023-11-17 DOI: 10.1007/s10440-023-00622-1
Qingyou He, Hai-Liang Li, Benoît Perthame
{"title":"Incompressible Limits of the Patlak-Keller-Segel Model and Its Stationary State","authors":"Qingyou He,&nbsp;Hai-Liang Li,&nbsp;Benoît Perthame","doi":"10.1007/s10440-023-00622-1","DOIUrl":"10.1007/s10440-023-00622-1","url":null,"abstract":"<div><p>We complete previous results about the incompressible limit of both the <span>(n)</span>-dimensional <span>((ngeq 3))</span> compressible Patlak-Keller-Segel (PKS) model and its stationary state. As in previous works, in this limit, we derive the weak form of a geometric free boundary problem of Hele-Shaw type, also called congested flow. In particular, we are able to take into account the unsaturated zone, and establish the complementarity relation which describes the limit pressure by a degenerate elliptic equation. Not only our analysis uses a completely different framework than previous approaches, but we also establish two novel uniform estimates in <span>(L^{3})</span> of the pressure gradient and in <span>(L^{1})</span> for the time derivative of the pressure. We also prove regularity à la Aronson-Bénilan. Furthermore, for the Hele-Shaw problem, we prove the uniqueness of solutions, meaning that the incompressible limit of the PKS model is unique. In addition, we establish the corresponding incompressible limit of the stationary state for the PKS model with a given mass, where, different from the case of PKS model, we obtain the uniform bound of pressure and the uniformly bounded support of density.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"188 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138138505","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: 7
Stability of a Vector-Borne Disease Model with a Delayed Nonlinear Incidence 一类具有时滞非线性发病率的病媒传播疾病模型的稳定性
IF 1.6 4区 数学
Acta Applicandae Mathematicae Pub Date : 2023-11-14 DOI: 10.1007/s10440-023-00623-0
Ali Traoré
{"title":"Stability of a Vector-Borne Disease Model with a Delayed Nonlinear Incidence","authors":"Ali Traoré","doi":"10.1007/s10440-023-00623-0","DOIUrl":"10.1007/s10440-023-00623-0","url":null,"abstract":"<div><p>A vector-borne disease model with spatial diffusion with time delays and a general incidence function is studied. We derived conditions under which the system exhibits threshold behavior. The stability of the disease-free equilibrium and the endemic equilibrium are analyzed by using the linearization method and constructing appropriate Lyapunov functionals. It is shown that the given conditions are satisfied by at least two common forms of the incidence function.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"188 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796466","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
On Cumulative Tsallis Entropies 论累积萨利斯熵
IF 1.6 4区 数学
Acta Applicandae Mathematicae Pub Date : 2023-11-13 DOI: 10.1007/s10440-023-00620-3
Thomas Simon, Guillaume Dulac
{"title":"On Cumulative Tsallis Entropies","authors":"Thomas Simon,&nbsp;Guillaume Dulac","doi":"10.1007/s10440-023-00620-3","DOIUrl":"10.1007/s10440-023-00620-3","url":null,"abstract":"<div><p>We investigate the cumulative Tsallis entropy, an information measure recently introduced as a cumulative version of the classical Tsallis differential entropy, which is itself a generalization of the Boltzmann-Gibbs statistics. This functional is here considered as a perturbation of the expected mean residual life via some power weight function. This point of view leads to the introduction of the dual cumulative Tsallis entropy and of two families of coherent risk measures generalizing those built on mean residual life. We characterize the finiteness of the cumulative Tsallis entropy in terms of <span>({mathcal{L}}_{p})</span>-spaces and show how they determine the underlying distribution. The range of the functional is exactly described under various constraints, with optimal bounds improving on all those previously available in the literature. Whereas the maximization of the Tsallis differential entropy gives rise to the classical <span>(q)</span>-Gaussian distribution which is a generalization of the Gaussian having a finite range or heavy tails, the maximization of the cumulative Tsallis entropy leads to an analogous perturbation of the Logistic distribution.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"188 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134796492","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: 1
Stability by Polynomial Squeezing for a Class of Energy Damping Plate Models 一类能量阻尼板模型的多项式压缩稳定性
IF 1.6 4区 数学
Acta Applicandae Mathematicae Pub Date : 2023-11-07 DOI: 10.1007/s10440-023-00619-w
Flank D. M. Bezerra, Linfang Liu, Vando Narciso
{"title":"Stability by Polynomial Squeezing for a Class of Energy Damping Plate Models","authors":"Flank D. M. Bezerra,&nbsp;Linfang Liu,&nbsp;Vando Narciso","doi":"10.1007/s10440-023-00619-w","DOIUrl":"10.1007/s10440-023-00619-w","url":null,"abstract":"<div><p>In this work we consider a semilinear plate equation with non-constant material density in the context of energy damping models. Existence and uniqueness of regular and generalized solutions are established. The energy associated to this equation is shown to posses a compressed polynomial decay range.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"188 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134795806","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
Bistability and Oscillatory Behaviours of Cyclic Feedback Loops 循环反馈回路的双稳性和振荡性
IF 1.6 4区 数学
Acta Applicandae Mathematicae Pub Date : 2023-10-31 DOI: 10.1007/s10440-023-00618-x
Jules Guilberteau
{"title":"Bistability and Oscillatory Behaviours of Cyclic Feedback Loops","authors":"Jules Guilberteau","doi":"10.1007/s10440-023-00618-x","DOIUrl":"10.1007/s10440-023-00618-x","url":null,"abstract":"<div><p>In this paper, we study the stability of an Ordinary Differential Equation (ODE) usually referred to as Cyclic Feedback Loop, which typically models a biological network of <span>(d)</span> molecules where each molecule regulates its successor in a cycle (<span>(A_{1}rightarrow A_{2}rightarrow cdots rightarrow A_{d-1} rightarrow A_{d} rightarrow A_{1})</span>). Regulations, which can be either positive or negative, are modelled by increasing or decreasing functions. We make an analysis of this model for a wide range of functions (including affine and Hill functions) by determining the parameters for which bistability and oscillatory behaviours arise. These results encompass previous theoretical studies of gene regulatory networks, which are particular cases of this model.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"188 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797897","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
Detached Shock Past a Blunt Body 经过钝体的分离电击
IF 1.6 4区 数学
Acta Applicandae Mathematicae Pub Date : 2023-10-31 DOI: 10.1007/s10440-023-00617-y
Myoungjean Bae, Wei Xiang
{"title":"Detached Shock Past a Blunt Body","authors":"Myoungjean Bae,&nbsp;Wei Xiang","doi":"10.1007/s10440-023-00617-y","DOIUrl":"10.1007/s10440-023-00617-y","url":null,"abstract":"<div><p>In <span>(mathbb{R}^{2})</span>, a symmetric blunt body <span>(W_{b})</span> is fixed by smoothing out the tip of a symmetric wedge <span>(W_{0})</span> with the half-wedge angle <span>(theta _{w}in (0, frac{pi }{2}))</span>. We first show that if a horizontal supersonic flow of uniform state moves toward <span>(W_{0})</span> with a Mach number <span>(M_{infty }&gt;1)</span> being sufficiently large depending on <span>(theta _{w})</span>, then the half-wedge angle <span>(theta _{w})</span> is less than <i>the detachment angle</i> so that there exist two shock solutions, <i>a weak shock solution and a strong shock solution</i>, with the shocks being straight and attached to the vertex of the wedge <span>(W_{0})</span>. Such shock solutions are given by a shock polar analysis, and they satisfy entropy conditions. The main goal of this work is to construct a detached shock solution of the steady Euler system for inviscid compressible irrotational flow in <span>(mathbb{R}^{2}setminus W_{b})</span>. Especially, we seek a shock solution with the far-field state given as the strong shock solution obtained from the shock polar analysis. Furthermore, we prove that the detached shock forms a convex curve around the blunt body <span>(W_{b})</span> if the Mach number of the incoming supersonic flow is sufficiently large, and if the boundary of <span>(W_{b})</span> is convex.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"188 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134797858","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: 2
Existence of Signed and Sign-Changing Solutions for Weighted Kirchhoff Problems with Critical Exponential Growth 临界指数增长加权Kirchhoff问题有符号解和变符号解的存在性
IF 1.6 4区 数学
Acta Applicandae Mathematicae Pub Date : 2023-10-24 DOI: 10.1007/s10440-023-00616-z
Brahim Dridi, Rached Jaidane, Rima Chetouane
{"title":"Existence of Signed and Sign-Changing Solutions for Weighted Kirchhoff Problems with Critical Exponential Growth","authors":"Brahim Dridi,&nbsp;Rached Jaidane,&nbsp;Rima Chetouane","doi":"10.1007/s10440-023-00616-z","DOIUrl":"10.1007/s10440-023-00616-z","url":null,"abstract":"<div><p>This work is devoted to study the existence of least energy sign-changing solutions for a nonlocal weighted Schrödinger-Kirchhoff problem in the unit ball <span>(B)</span> of <span>(mathbb{R}^{N})</span>, <span>(N&gt;2)</span>. The non-linearity of the equation is assumed to have exponential growth in view of Trudinger-Moser type inequalities. In order to obtain our existence result, we use the constrained minimization in Nehari set, the quantitative deformation Lemma and degree theory results.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"188 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50046340","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
Concentration Phenomena of Riemann Solutions to a Logarithmic Perturbed Model 对数摄动模型的Riemann解的集中现象
IF 1.6 4区 数学
Acta Applicandae Mathematicae Pub Date : 2023-10-18 DOI: 10.1007/s10440-023-00615-0
Shiwei Li
{"title":"Concentration Phenomena of Riemann Solutions to a Logarithmic Perturbed Model","authors":"Shiwei Li","doi":"10.1007/s10440-023-00615-0","DOIUrl":"10.1007/s10440-023-00615-0","url":null,"abstract":"<div><p>Introducing a logarithmic pressure, we analyze the phenomenon of concentration and the formation of delta-shocks for the generalized Chaplygin gas dynamics. We first solve the Riemann problem for the logarithmic perturbed model and construct the solutions with four kinds of structures <span>(R_{1}+R_{2})</span>, <span>(R_{1}+S_{2})</span>, <span>(S_{1}+R_{2})</span> and <span>(S_{1}+S_{2})</span>. Then it is shown that when the logarithmic pressure vanishes, the limits of the Riemann solutions for the logarithmic perturbed model are just these of the generalized Chaplygin gas dynamics. In particular, when the initial data satisfy some certain conditions, the <span>(S_{1}+S_{2})</span> solution of the logarithmic perturbed model tends to the delta-shock solution of the generalized Chaplygin gas dynamics. Finally, some numerical results exhibit the process of formation of delta-shocks.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"188 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10440-023-00615-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50036843","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
Principal and Nonprincipal Solutions of Impulsive Dynamic Equations: Leighton and Wong Type Oscillation Theorems 脉冲动力方程的主解和非主解:Leighton和Wong型振荡定理
IF 1.6 4区 数学
Acta Applicandae Mathematicae Pub Date : 2023-10-17 DOI: 10.1007/s10440-023-00614-1
A. Zafer, S. Doğru Akgöl
{"title":"Principal and Nonprincipal Solutions of Impulsive Dynamic Equations: Leighton and Wong Type Oscillation Theorems","authors":"A. Zafer,&nbsp;S. Doğru Akgöl","doi":"10.1007/s10440-023-00614-1","DOIUrl":"10.1007/s10440-023-00614-1","url":null,"abstract":"<div><p>Principal and nonprincipal solutions of differential equations play a critical role in studying the qualitative behavior of solutions in numerous related differential equations. The existence of such solutions and their applications are already documented in the literature for differential equations, difference equations, dynamic equations, and impulsive differential equations. In this paper, we make a contribution to this field by examining impulsive dynamic equations and proving the existence of such solutions for second-order impulsive dynamic equations. As an illustration, we prove the famous Leighton and Wong oscillation theorems for impulsive dynamic equations. Furthermore, we provide supporting examples to demonstrate the relevance and effectiveness of the results.</p></div>","PeriodicalId":53132,"journal":{"name":"Acta Applicandae Mathematicae","volume":"188 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-10-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50035032","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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