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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":"41 2 1","pages":""},"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
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":"37 1","pages":""},"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":"55 1","pages":""},"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":"82 1","pages":""},"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
Travelling Waves in a PDE-ODE Coupled Model of Cellulolytic Biofilms with Nonlinear Diffusion. 具有非线性扩散的细胞溶解生物膜PDE–ODE耦合模型中的行波
IF 1.4 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-01-01 Epub Date: 2023-01-18 DOI: 10.1007/s10884-022-10240-4
K Mitra, J M Hughes, S Sonner, H J Eberl, J D Dockery
{"title":"Travelling Waves in a PDE-ODE Coupled Model of Cellulolytic Biofilms with Nonlinear Diffusion.","authors":"K Mitra, J M Hughes, S Sonner, H J Eberl, J D Dockery","doi":"10.1007/s10884-022-10240-4","DOIUrl":"10.1007/s10884-022-10240-4","url":null,"abstract":"<p><p>We analyze travelling wave (TW) solutions for nonlinear systems consisting of an ODE coupled to a degenerate PDE with a diffusion coefficient that vanishes as the solution tends to zero and blows up as it approaches its maximum value. Stable TW solutions for such systems have previously been observed numerically as well as in biological experiments on the growth of cellulolytic biofilms. In this work, we provide an analytical justification for these observations and prove existence and stability results for TW solutions of such models. Using the TW ansatz and a first integral, the system is reduced to an autonomous dynamical system with two unknowns. Analysing the system in the corresponding phase-plane, the existence of a unique TW is shown, which possesses a sharp front and a diffusive tail, and is moving with a constant speed. The linear stability of the TW in two space dimensions is proven under suitable assumptions on the initial data. Finally, numerical simulations are presented that affirm the theoretical predictions on the existence, stability, and parametric dependence of the travelling waves.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"1 1","pages":"3037-3071"},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11564301/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44342933","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
Regularization by Noise of an Averaged Version of the Navier-Stokes Equations. Navier-Stokes方程平均版本的噪声正则化
IF 1.4 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-01-01 Epub Date: 2023-03-28 DOI: 10.1007/s10884-023-10255-5
Theresa Lange
{"title":"Regularization by Noise of an Averaged Version of the Navier-Stokes Equations.","authors":"Theresa Lange","doi":"10.1007/s10884-023-10255-5","DOIUrl":"10.1007/s10884-023-10255-5","url":null,"abstract":"<p><p>In Tao 2016, the author constructs an averaged version of the deterministic three-dimensional Navier-Stokes equations (3D NSE) which experiences blow-up in finite time. In the last decades, various works have studied suitable perturbations of ill-behaved deterministic PDEs in order to prevent or delay such behavior. A promising example is given by a particular choice of stochastic transport noise closely studied in Flandoli et al. 2021. We analyze the model in Tao 2016 in view of these results and discuss the regularization skills of this noise in the context of the averaged 3D NSE.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"1 1","pages":"3011-3036"},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11564229/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45348581","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
Well-Posedness Properties for a Stochastic Rotating Shallow Water Model. 随机旋转浅水模型的适定性
IF 1.4 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-01-01 Epub Date: 2023-01-20 DOI: 10.1007/s10884-022-10243-1
Dan Crisan, Oana Lang
{"title":"Well-Posedness Properties for a Stochastic Rotating Shallow Water Model.","authors":"Dan Crisan, Oana Lang","doi":"10.1007/s10884-022-10243-1","DOIUrl":"10.1007/s10884-022-10243-1","url":null,"abstract":"<p><p>In this paper, we study the well-posedness properties of a stochastic rotating shallow water system. An inviscid version of this model has first been derived in Holm (Proc R Soc A 471:20140963, 2015) and the noise is chosen according to the Stochastic Advection by Lie Transport theory presented in Holm (Proc R Soc A 471:20140963, 2015). The system is perturbed by noise modulated by a function that is not Lipschitz in the norm where the well-posedness is sought. We show that the system admits a unique maximal solution which depends continuously on the initial condition. We also show that the interval of existence is strictly positive and the solution is global with positive probability.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"1 1","pages":"3175-3205"},"PeriodicalIF":1.4,"publicationDate":"2024-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11564351/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45441867","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
The Stability Region for Schur Stable Trinomials with General Complex Coefficients 具有一般复数系数的舒尔稳定三项式的稳定区域
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2023-12-16 DOI: 10.1007/s10884-023-10331-w
Gerardo Barrera, Waldemar Barrera, Juan Pablo Navarrete
{"title":"The Stability Region for Schur Stable Trinomials with General Complex Coefficients","authors":"Gerardo Barrera, Waldemar Barrera, Juan Pablo Navarrete","doi":"10.1007/s10884-023-10331-w","DOIUrl":"https://doi.org/10.1007/s10884-023-10331-w","url":null,"abstract":"<p>In this paper, we characterize the stability region for trinomials of the form <span>(f(zeta ):=azeta ^n + bzeta ^m +c)</span>, <span>(zeta in mathbb {C})</span>, where <i>a</i>, <i>b</i> and <i>c</i> are non-zero complex numbers and <span>(n,min mathbb {N})</span> with <span>(n&gt;m)</span>. More precisely, we provide necessary and sufficient conditions on the coefficients <i>a</i>, <i>b</i> and <i>c</i> in order that all the roots of the trinomial <i>f</i> belongs to the open unit disc in the complex plane. The proof is based on Bohl’s Theorem (Bohl in Math Ann 65(4):556–566, 1908) introduced in 1908.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"4 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138686974","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 Szymczak Functor and Shift Equivalence on the Category of Finite Sets and Finite Relations 有限集和有限关系范畴上的西姆扎克函数和移位等价性
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2023-12-09 DOI: 10.1007/s10884-023-10332-9
Mateusz Przybylski, Marian Mrozek, Jim Wiseman
{"title":"The Szymczak Functor and Shift Equivalence on the Category of Finite Sets and Finite Relations","authors":"Mateusz Przybylski, Marian Mrozek, Jim Wiseman","doi":"10.1007/s10884-023-10332-9","DOIUrl":"https://doi.org/10.1007/s10884-023-10332-9","url":null,"abstract":"<p>The construction of the Conley index for dynamical systems with discrete time requires an equivalence relation between morphisms induced on index pairs. It follows from the features of the Szymczak functor that shift equivalence, whose equivalence classes are the isomorphism classes in the Szymczak category, is the most general equivalence available. In the case of dynamics modeled from data, the morphisms induced on index pairs are relations. We present an algorithmizable classification of shift equivalence classes for the category of finite sets with arbitrary relations as morphisms. The research is the first step towards the construction of a Conley theory for relations.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"19 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138563435","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
Hypocoercivity in Algebraically Constrained Partial Differential Equations with Application to Oseen Equations 代数约束偏微分方程中的超矫顽力及其在奥森方程中的应用
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2023-12-08 DOI: 10.1007/s10884-023-10327-6
Franz Achleitner, Anton Arnold, Volker Mehrmann
{"title":"Hypocoercivity in Algebraically Constrained Partial Differential Equations with Application to Oseen Equations","authors":"Franz Achleitner, Anton Arnold, Volker Mehrmann","doi":"10.1007/s10884-023-10327-6","DOIUrl":"https://doi.org/10.1007/s10884-023-10327-6","url":null,"abstract":"<p>The long-time behavior of solutions to different versions of Oseen equations of fluid flow on the 2D torus is analyzed using the concept of hypocoercivity. The considered models are isotropic Oseen equations where the viscosity acts uniformly in all directions and anisotropic Oseen-type equations with different viscosity directions. The hypocoercivity index is determined (if it exists) and it is shown that similar to the finite dimensional case of ordinary differential equations and differential-algebraic equations it characterizes its decay behavior.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"9 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2023-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138553371","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
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