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Traveling Phase Interfaces in Viscous Forward–Backward Diffusion Equations 粘性正反向扩散方程中的移动相界面
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-08-17 DOI: 10.1007/s10884-024-10382-7
Carina Geldhauser, Michael Herrmann, Dirk Janßen
{"title":"Traveling Phase Interfaces in Viscous Forward–Backward Diffusion Equations","authors":"Carina Geldhauser, Michael Herrmann, Dirk Janßen","doi":"10.1007/s10884-024-10382-7","DOIUrl":"https://doi.org/10.1007/s10884-024-10382-7","url":null,"abstract":"<p>The viscous regularization of an ill-posed diffusion equation with bistable nonlinearity predicts a hysteretic behavior of dynamical phase transitions but a complete mathematical understanding of the intricate multiscale evolution is still missing. We shed light on the fine structure of propagating phase boundaries by carefully examining traveling wave solutions in a special case. Assuming a trilinear constitutive relation we characterize all waves that possess a monotone profile and connect the two phases by a single interface of positive width. We further study the two sharp-interface regimes related to either vanishing viscosity or the bilinear limit.\u0000</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"24 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212512","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
A Simple Approach to Stability of Semi-wavefronts in Parabolic-Difference Systems 抛物-差分系统中半波前稳定性的简单方法
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-08-13 DOI: 10.1007/s10884-024-10371-w
Abraham Solar
{"title":"A Simple Approach to Stability of Semi-wavefronts in Parabolic-Difference Systems","authors":"Abraham Solar","doi":"10.1007/s10884-024-10371-w","DOIUrl":"https://doi.org/10.1007/s10884-024-10371-w","url":null,"abstract":"<p>We consider the parabolic-difference system <span>( Big ({dot{u}}(t,x), v(t, x)Big )=Big (D, u_{xx}(t, x)hspace{-0.06cm}-hspace{-0.06cm}f(u(t, x))+Hv(t-h, cdot )(x), ,, g(u(t, x))+B v(t-h, cdot )(x)Big ))</span>, <span>( t&gt;0, xin {{mathbb {R}}},)</span> which appears in a model for hematopoietic cells population. We prove the global stability of semi-wavefronts <span>((phi _c, varphi _c))</span> for this system. More precisely, for an initial history <span>((u_0, v_0))</span> we study the convergence to zero of the associated perturbation <span>(P(t)=(u(t)-phi _c, v(t)-varphi _c))</span>, as <span>(trightarrow +infty )</span>, in a suitable Banach space <i>Y</i>; we prove that if the initial perturbation satisfies <span>(P_0in C([-h, 0], Y))</span>, then <span>(P(t)rightarrow 0)</span> in two cases: (i) <span>(v_0=varphi _c)</span>, for all <span>(hge 0)</span> or (ii) <span>(v_0not equiv varphi _c)</span> for all <span>(hle h_*)</span> and some <span>(h_*=h_*(B))</span>. This result is obtained by analyzing an abstract integral equation with infinite delay. Also, our main result allow us to obtain a result about the uniqueness of these semi-wavefronts.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"9 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212511","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
Local Well-Posedness of the Nonlinear Wave System Near a Space Corner of Right Angle 直角空间角附近非线性波系统的局部良好拟合
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-08-12 DOI: 10.1007/s10884-024-10386-3
Feng Xiao
{"title":"Local Well-Posedness of the Nonlinear Wave System Near a Space Corner of Right Angle","authors":"Feng Xiao","doi":"10.1007/s10884-024-10386-3","DOIUrl":"https://doi.org/10.1007/s10884-024-10386-3","url":null,"abstract":"<p>We are concerned with the well-posedness of the nonlinear wave system, which is a first-order hyperbolic system, in the vicinity of a right-angled spatial corner. The problem can be expressed as an initial boundary value problem (IBVP) involving a second-order hyperbolic equation in a spatial domain with a corner. The main difficulty in establishing the local well-posedness of the problem arises from the lack of smoothness in the spatial domain due to the presence of the corner point. Additionally, the Neumann-type boundary conditions on both edges of the corner angle do not satisfy the linear stability condition, posing challenges in obtaining higher-order a priori estimates for the boundary terms in the analysis. To address the corner singularity, modified extension methods will be employed in this paper. Furthermore, new techniques will be developed to control the boundary terms, leveraging the observation that the boundary operators are co-normal.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"22 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212580","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
Global Existence for Long Wave Hopf Unstable Spatially Extended Systems with a Conservation Law 具有守恒定律的长波霍普夫不稳定空间扩展系统的全局存在性
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-08-07 DOI: 10.1007/s10884-024-10380-9
Nicole Gauss, Anna Logioti, Guido Schneider, Dominik Zimmermann
{"title":"Global Existence for Long Wave Hopf Unstable Spatially Extended Systems with a Conservation Law","authors":"Nicole Gauss, Anna Logioti, Guido Schneider, Dominik Zimmermann","doi":"10.1007/s10884-024-10380-9","DOIUrl":"https://doi.org/10.1007/s10884-024-10380-9","url":null,"abstract":"<p>We are interested in reaction–diffusion systems, with a conservation law, exhibiting a Hopf bifurcation at the spatial wave number <span>( k = 0 )</span>. With the help of a multiple scaling perturbation ansatz a Ginzburg–Landau equation coupled to a scalar conservation law can be derived as an amplitude system for the approximate description of the dynamics of the original reaction–diffusion system near the first instability. We use the amplitude system to show the global existence of all solutions starting in a small neighborhood of the weakly unstable ground state for original systems posed on a large spatial interval with periodic boundary conditions.\u0000</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"3 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141930931","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
Global Existence and Some Qualitative Properties of Weak Solutions for a Class of Heat Equations with a Logarithmic Nonlinearity in Whole $${mathbb {R}}^{N}$$ 全$${{mathbb {R}}^{N}$ 具有对数非线性的一类热方程弱解的全局存在性和一些定性性质
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-08-06 DOI: 10.1007/s10884-024-10385-4
Tahir Boudjeriou, Claudianor O. Alves
{"title":"Global Existence and Some Qualitative Properties of Weak Solutions for a Class of Heat Equations with a Logarithmic Nonlinearity in Whole $${mathbb {R}}^{N}$$","authors":"Tahir Boudjeriou, Claudianor O. Alves","doi":"10.1007/s10884-024-10385-4","DOIUrl":"https://doi.org/10.1007/s10884-024-10385-4","url":null,"abstract":"<p>This paper aims to investigate the global existence and uniqueness of weak solutions for a class of heat equations with logarithmic nonlinearity in <span>({mathbb {R}}^{N})</span>, as well as to examine some of their qualitative properties. Additionally, we analyze the boundedness and higher integrability of these solutions.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"16 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141931011","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
Traveling Wavefronts to a Model of Precursor and Differentiated Cells: Impacting Parameter-Structure Transition from Monostable to Bistable, and from Monotone to Non-monotone 前体细胞和分化细胞模型的移动波面：从单稳态到双稳态以及从单调到非单调的参数-结构转变的影响
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-08-06 DOI: 10.1007/s10884-024-10384-5
Yuanxi Yue, Chunhua Ou
{"title":"Traveling Wavefronts to a Model of Precursor and Differentiated Cells: Impacting Parameter-Structure Transition from Monostable to Bistable, and from Monotone to Non-monotone","authors":"Yuanxi Yue, Chunhua Ou","doi":"10.1007/s10884-024-10384-5","DOIUrl":"https://doi.org/10.1007/s10884-024-10384-5","url":null,"abstract":"<p>This paper provides a novel analysis of the rich and complex propagation dynamics to a model of precursor and differentiated cells, with the appearance of non-isolated equilibria on a line in the phase space. We established the existence of traveling waves in the monostable monotone case by means of continuation argument via perturbation in a weighted functional space, by applying the abstract implicit function theorem. We proved necessary and sufficient conditions of the minimal wave speed selection and showed the existence of the transition (turning point) <span>(k^*)</span> for the minimal wave speed when the parameters <span>(lambda )</span> and <span>(gamma )</span> are fixed. Two explicit estimates about <span>(k^*)</span> were given by the easy-to-apply theorem we derived. We investigated the decay rate of the minimal traveling wave as <span>(zrightarrow infty )</span> in terms of the value of <i>k</i>. We further proved the existence of non-negative wavefronts in the monostable non-monotone case and found that the minimal wave speed is always linearly selected. Finally in the bistable monotone case, the existence and uniqueness of bistable traveling waves were proved via constructing an auxiliary parabolic non-local equation.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"11 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141931008","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
Entropy for Three-dimensional Vector Fields 三维矢量场的熵
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-08-03 DOI: 10.1007/s10884-024-10383-6
Fei Li, Wanlou Wu
{"title":"Entropy for Three-dimensional Vector Fields","authors":"Fei Li, Wanlou Wu","doi":"10.1007/s10884-024-10383-6","DOIUrl":"https://doi.org/10.1007/s10884-024-10383-6","url":null,"abstract":"<p>In this paper, we show that for any <span>(C^1)</span> three-dimensional vector fields with positive topological entropy, the topological entropy can be approximated by horseshoes. Precisely, for any <span>(C^1)</span> three-dimensional vector field <i>X</i> with positive topological entropy, there exists a vector field <i>Y</i> arbitrarily close (in the <span>(C^1)</span> topology) to <i>X</i> exhibiting a horseshoe <span>(Lambda )</span> such that the topological entropy of <i>Y</i> restricted on <span>(Lambda )</span> can arbitrarily approximate the topological entropy of <i>X</i>. This extends a classical result (Katok in Inst Hautes Études Sci Publ Math 51:137–173, 1980) of Katok for <span>(C^{1+alpha }(alpha &gt;0))</span> surface diffeomorphisms and a result (Wu and Liu in Proc Am Math Soc 148(1):223–233, 2020) for <span>(C^1)</span> surface diffeomorphisms.\u0000</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"217 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141884929","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
Pinsker $$sigma $$ -Algebra Character and Mean Li–Yorke Chaos Pinsker $$sigma $$ -代数特性与平均李-约克混沌
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-07-22 DOI: 10.1007/s10884-024-10381-8
Chunlin Liu, Rongzhong Xiao, Leiye Xu
{"title":"Pinsker $$sigma $$ -Algebra Character and Mean Li–Yorke Chaos","authors":"Chunlin Liu, Rongzhong Xiao, Leiye Xu","doi":"10.1007/s10884-024-10381-8","DOIUrl":"https://doi.org/10.1007/s10884-024-10381-8","url":null,"abstract":"<p>Let <i>G</i> be an infinite countable discrete amenable group. For any <i>G</i>-action on a compact metric space <i>X</i>, it is proved that for any sequence <span>((G_n)_{nge 1})</span> consisting of non-empty finite subsets of <i>G</i> with <span>(lim _{nrightarrow infty }|G_n|=infty )</span>, Pinsker <span>(sigma )</span>-algebra is a characteristic factor for <span>((G_n)_{nge 1})</span>. As a consequence, for a class of <i>G</i>-topological dynamical systems, positive topological entropy implies mean Li–Yorke chaos along a class of sequences consisting of non-empty finite subsets of <i>G</i>.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"104 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744186","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
Entropy Spectrum of Lyapunov Exponents for Typical Cocycles 典型循环的李亚普诺夫指数熵谱
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-07-20 DOI: 10.1007/s10884-024-10379-2
Reza Mohammadpour
{"title":"Entropy Spectrum of Lyapunov Exponents for Typical Cocycles","authors":"Reza Mohammadpour","doi":"10.1007/s10884-024-10379-2","DOIUrl":"https://doi.org/10.1007/s10884-024-10379-2","url":null,"abstract":"<p>In this paper, we study the size of the level sets of all Lyapunov exponents. For typical cocycles, we establish a variational relation between the topological entropy of the level sets of Lyapunov exponents and the topological pressure of the generalized singular value function.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"64 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141744188","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
Generalized Bounded Distortion Property 广义有界失真特性
IF 1.3 4区 数学
Journal of Dynamics and Differential Equations Pub Date : 2024-07-05 DOI: 10.1007/s10884-024-10376-5
Gregory Borissov, Grigorii Monakov
{"title":"Generalized Bounded Distortion Property","authors":"Gregory Borissov, Grigorii Monakov","doi":"10.1007/s10884-024-10376-5","DOIUrl":"https://doi.org/10.1007/s10884-024-10376-5","url":null,"abstract":"<p>We prove the nonstationary bounded distortion property for <span>(C^{1 + varepsilon })</span> smooth dynamical systems on multidimensional spaces. The results we obtain are motivated by potential application to study of spectral properties of discrete Schrödinger operators with potentials generated by Sturmian sequences.</p>","PeriodicalId":15624,"journal":{"name":"Journal of Dynamics and Differential Equations","volume":"10 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141551893","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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