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Journal of Dynamics and Differential Equations最新文献

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Shadowing for Local Homeomorphisms, with Applications to Edge Shift Spaces of Infinite Graphs 局部同构的阴影，及其在无限图边缘移动空间中的应用
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-01-28 DOI: 10.1007/s10884-023-10342-7
Daniel Gonçalves, Bruno B. Uggioni
{"title":"Shadowing for Local Homeomorphisms, with Applications to Edge Shift Spaces of Infinite Graphs","authors":"Daniel Gonçalves, Bruno B. Uggioni","doi":"10.1007/s10884-023-10342-7","DOIUrl":"https://doi.org/10.1007/s10884-023-10342-7","url":null,"abstract":"<p>In this paper, we develop the basic theory of the shadowing property for local homeomorphisms of metric locally compact spaces, with a focus on applications to edge shift spaces connected with C*-algebra theory. For the local homeomorphism (the Deaconu–Renault system) associated with a directed graph, we completely characterize the shadowing property in terms of conditions on sets of paths. Using these results, we single out classes of graphs for which the associated system presents the shadowing property, fully characterize the shadowing property for systems associated with certain graphs, and show that the system associated with the rose of infinite petals presents the shadowing property and that the Renewal shift system does not present the shadowing property.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139583508","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
Continuity of the Unbounded Attractors for a Fractional Perturbation of a Scalar Reaction-Diffusion Equation 标量反应-扩散方程的分数扰动的无界吸引子的连续性
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-01-23 DOI: 10.1007/s10884-023-10341-8
Maykel Belluzi, Matheus C. Bortolan, Ubirajara Castro, Juliana Fernandes
{"title":"Continuity of the Unbounded Attractors for a Fractional Perturbation of a Scalar Reaction-Diffusion Equation","authors":"Maykel Belluzi, Matheus C. Bortolan, Ubirajara Castro, Juliana Fernandes","doi":"10.1007/s10884-023-10341-8","DOIUrl":"https://doi.org/10.1007/s10884-023-10341-8","url":null,"abstract":"<p>In this work we study the continuity (both upper and lower semicontinuity), defined using the Hausdorff semidistance, of the unbounded attractors for a family of fractional perturbations of a scalar reaction-diffusion equation with a non-dissipative nonlinear term.\u0000</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139554229","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
Hyperbolicity and Rigidity for Fibred Partially Hyperbolic Systems 纤维部分双曲系统的双曲性和刚性
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-01-23 DOI: 10.1007/s10884-023-10343-6
Sankhadip Chakraborty, Marcelo Viana
{"title":"Hyperbolicity and Rigidity for Fibred Partially Hyperbolic Systems","authors":"Sankhadip Chakraborty, Marcelo Viana","doi":"10.1007/s10884-023-10343-6","DOIUrl":"https://doi.org/10.1007/s10884-023-10343-6","url":null,"abstract":"<p>Every volume-preserving accessible centre-bunched fibred partially hyperbolic system with 2-dimensional centre either (a) has two distinct centre Lyapunov exponents, or (b) exhibits an invariant continuous line field (or pair of line fields) tangent to the centre leaves, or (c) admits a continuous conformal structure on the centre leaves invariant under both the dynamics and the stable and unstable holonomies. The last two alternatives carry strong restrictions on the topology of the centre leaves: (b) can only occur on tori, and for (c) the centre leaves must be either tori or spheres. Moreover, under some additional conditions, such maps are rigid, in the sense that they are topologically conjugate to specific algebraic models. When the system is symplectic (a) implies that the centre Lyapunov exponents are non-zero, and thus the system is (non-uniformly) hyperbolic.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139554447","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
Comment on: Criteria for Strong and Weak Random Attractors 评论强弱随机吸引力的标准
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-01-23 DOI: 10.1007/s10884-023-10316-9
Hans Crauel, Sarah Geiss, Michael Scheutzow
{"title":"Comment on: Criteria for Strong and Weak Random Attractors","authors":"Hans Crauel, Sarah Geiss, Michael Scheutzow","doi":"10.1007/s10884-023-10316-9","DOIUrl":"https://doi.org/10.1007/s10884-023-10316-9","url":null,"abstract":"<p>In the article ’Criteria for Strong and Weak Random Attractors’ necessary and sufficient conditions for strong attractors and weak attractors are studied. In this note we correct two of its theorems on strong attractors.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139554398","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
Delta Shocks as Solutions of Conservation Laws with Discontinuous Moving Source 三角冲击作为不连续移动源的守恒定律解
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-01-22 DOI: 10.1007/s10884-023-10338-3
C. O. R. Sarrico
{"title":"Delta Shocks as Solutions of Conservation Laws with Discontinuous Moving Source","authors":"C. O. R. Sarrico","doi":"10.1007/s10884-023-10338-3","DOIUrl":"https://doi.org/10.1007/s10884-023-10338-3","url":null,"abstract":"<p>A Riemann problem for the conservation law <span>(u_{t}+[phi (u)]_{x}=kH(x-vt))</span>, where <i>x</i>, <i>t</i>, <i>k</i>, <i>v</i> and <span>(u=u(x,t))</span> are real numbers, is studied with the goal of getting singular solutions in a convenient space of distributions that contains delta shock waves. Here <span>(phi )</span> stands for an entire function taking real values on the real axis and <i>H</i> represents the Heaviside function. When <i>u</i> is seen as a density of matter some surprises may appear such as the creation of matter from a vacuum state. In a particular case, as the time goes on, such a matter grows continuously, running away from any spatial bounded region, what can be viewed as a unidimensional model of universe.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139514788","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
The Existence of Isolating Blocks for Multivalued Semiflows 多值半流体隔离块的存在性
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-01-19 DOI: 10.1007/s10884-023-10339-2
Estefani M. Moreira, José Valero
{"title":"The Existence of Isolating Blocks for Multivalued Semiflows","authors":"Estefani M. Moreira, José Valero","doi":"10.1007/s10884-023-10339-2","DOIUrl":"https://doi.org/10.1007/s10884-023-10339-2","url":null,"abstract":"<p>In this article, we show the existence of an isolating block, a special neighborhood of an isolated invariant set, for multivalued semiflows acting on metric spaces (not locally compact). Isolating blocks play an important role in Conley’s index theory for single-valued semiflows and are used to define the concepts of homology index. Although Conley’s index was generalized in the context of multivalued (semi) flows, the approaches skip the traditional construction made by Conley, and later, Rybakowski. Our aim is to present a theory of isolating blocks for multivalued semiflows in which we understand such a neighborhood of a weakly isolated invariant set in the same way as we understand it for invariant sets in the single-valued scenario. After that, we will apply this abstract result to a differential inclusion in order to show that we can construct isolating blocks for each equilibrium of the problem.\u0000</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139498762","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
Rayleigh–Bénard Convection with Stochastic Forcing Localised Near the Bottom 近底局部随机强迫的瑞利-贝纳德对流
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-01-19 DOI: 10.1007/s10884-023-10336-5
Juraj Földes, Armen Shirikyan
{"title":"Rayleigh–Bénard Convection with Stochastic Forcing Localised Near the Bottom","authors":"Juraj Földes, Armen Shirikyan","doi":"10.1007/s10884-023-10336-5","DOIUrl":"https://doi.org/10.1007/s10884-023-10336-5","url":null,"abstract":"<p>We prove stochastic stability of the three-dimensional Rayleigh–Bénard convection in the infinite Prandtl number regime for any pair of temperatures maintained on the top and the bottom. Assuming that the non-degenerate random perturbation acts in a thin layer adjacent to the bottom of the domain, we prove that the law of the random flow periodic in the two infinite directions stabilises to a unique stationary measure, provided that there is at least one point accessible from any initial state. We also prove that the latter property is satisfied if the amplitude of the noise is sufficiently large.\u0000</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139498858","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 of Global Entropy Solution for Eulerian Droplet Models and Two-phase Flow Model with Non-constant Air Velocity 欧拉液滴模型和气流速度不恒定的两相流模型的全局熵解的存在性
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-01-13 DOI: 10.1007/s10884-023-10337-4
Abhrojyoti Sen, Anupam Sen
{"title":"Existence of Global Entropy Solution for Eulerian Droplet Models and Two-phase Flow Model with Non-constant Air Velocity","authors":"Abhrojyoti Sen, Anupam Sen","doi":"10.1007/s10884-023-10337-4","DOIUrl":"https://doi.org/10.1007/s10884-023-10337-4","url":null,"abstract":"<p>This article addresses the question concerning the existence of global entropy solution for generalized Eulerian droplet models with air velocity depending on both space and time variables. When <span>(f(u)=u,)</span> <span>(kappa (t)=const.)</span> and <span>(u_a(x,t)=const.)</span> in (1.1), the study of the Riemann problem has been carried out by Keita and Bourgault (J Math Anal Appl 472(1):1001–1027, 2019) and Zhang et al. (Appl Anal 102(2):576–589, 2023). We show the global existence of the entropy solution to (1.1) for any strictly increasing function <span>(f(cdot ))</span> and <span>(u_a(x,t))</span> depending only on time with mild regularity assumptions on the initial data via <i>shadow wave tracking</i> approach. This represents a significant improvement over the findings of Yang (J Differ Equ 159(2):447–484, 1999). Next, by using the <i>generalized variational principle,</i> we prove the existence of an explicit entropy solution to (1.1) with <span>(f(u)=u,)</span> for all time <span>(t&gt;0)</span> and initial mass <span>(v_0&gt;0,)</span> where <span>(u_a(x,t))</span> depends on both space and time variables, and also has an algebraic decay in the time variable. This improves the results of many authors such as Ha et al. (J Differ Equ 257(5):1333–1371, 2014), Cheng and Yang (Appl Math Lett 135(6):8, 2023) and Ding and Wang (Quart Appl Math 62(3):509–528, 2004) in various ways. Furthermore, by employing the shadow wave tracking procedure, we discuss the existence of global entropy solution to the generalized two-phase flow model with time-dependent air velocity that extends the recent results of Shen and Sun (J Differ Equ 314:1–55, 2022).</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139464580","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
Dichotomies for Triangular Systems via Admissibility 通过可接受性实现三角形系统的二分法
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-01-13 DOI: 10.1007/s10884-023-10335-6
Davor Dragičević, Kenneth J. Palmer
{"title":"Dichotomies for Triangular Systems via Admissibility","authors":"Davor Dragičević, Kenneth J. Palmer","doi":"10.1007/s10884-023-10335-6","DOIUrl":"https://doi.org/10.1007/s10884-023-10335-6","url":null,"abstract":"<p>In this article we study the relationship between the exponential dichotomy properties of a triangular system of linear difference equations and its associated diagonal system. We use admissibility to give new shorter proofs of results obtained in Battelli et al. (J Differ Equ Appl 28:1054–1086, 2022) and we also establish new necessary and sufficient conditions that the diagonal system have a dichotomy when the triangular system has a dichotomy. We conclude with analogous results for differential equations.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139464497","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
Higher-Order Continuity of Pullback Random Attractors for Random Quasilinear Equations with Nonlinear Colored Noise 具有非线性彩色噪声的随机准线性方程的回拉随机吸引子的高阶连续性
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-01-10 DOI: 10.1007/s10884-023-10333-8
Yangrong Li, Fengling Wang, Tomás Caraballo
{"title":"Higher-Order Continuity of Pullback Random Attractors for Random Quasilinear Equations with Nonlinear Colored Noise","authors":"Yangrong Li, Fengling Wang, Tomás Caraballo","doi":"10.1007/s10884-023-10333-8","DOIUrl":"https://doi.org/10.1007/s10884-023-10333-8","url":null,"abstract":"<p>For a nonautonomous random dynamical system, we introduce a concept of a pullback random bi-spatial attractor (PRBA). We prove an existence theorem of a PRBA, which includes its measurability, compactness and attraction in the regular space. We then establish the residual dense continuity of a family of PRBAs from a parameter space into the space of all compact subsets of the regular space equipped by Hausdorff metric. The abstract results are illustrated in the nonautonomous random quasilinear equation driven by nonlinear colored noise, where the size of noise belongs to <span>((0,infty ])</span> and the infinite size corresponds to the deterministic equation. The application results are the existence and residual dense continuity of PRBAs on <span>((0,infty ])</span> in both square and <i>p</i>-order Lebesgue spaces, where <span>(p&gt;2)</span>. The lower semi-continuity of attractors in the regular space seems to be a new subject even for an autonomous deterministic system.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2024-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139421691","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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