Discrete & Continuous Dynamical Systems - S最新文献_第6页

A Cantor dynamical system is slow if and only if all its finite orbits are attracting 当且仅当康托动力系统的所有有限轨道都相互吸引时，康托动力系统是慢的

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-05-17 DOI: 10.3934/dcds.2022007

Silvère Gangloff, P. Oprocha

引用次数: 1

Optimal boundary regularity for some singular Monge-Ampère equations on bounded convex domains 有界凸域上奇异monge - ampantere方程的最优边界正则性

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-04-20 DOI: 10.3934/dcds.2021188

N. Le

引用次数: 4

Pure strictly uniform models of non-ergodic measure automorphisms 非遍历测度自同构的纯严格一致模型

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-04-19 DOI: 10.3934/dcds.2021140

T. Downarowicz, B. Weiss

引用次数: 3

A dissipative logarithmic-Laplacian type of plate equation: Asymptotic profile and decay rates 耗散对数-拉普拉斯型平板方程:渐近轮廓和衰减率

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-04-17 DOI: 10.3934/dcds.2021189

R. Charão, Alessandra Piske, R. Ikehata

{"title":"A dissipative logarithmic-Laplacian type of plate equation: Asymptotic profile and decay rates","authors":"R. Charão, Alessandra Piske, R. Ikehata","doi":"10.3934/dcds.2021189","DOIUrl":"https://doi.org/10.3934/dcds.2021189","url":null,"abstract":"We introduce a new model of the logarithmic type of wave like plate equation with a nonlocal logarithmic damping mechanism. We consider the Cauchy problem for this new model in <inline-formula><tex-math id=\"M1\">begin{document}$ {{bf R}}^{n} $end{document}</tex-math></inline-formula>, and study the asymptotic profile and optimal decay rates of solutions as <inline-formula><tex-math id=\"M2\">begin{document}$ t to infty $end{document}</tex-math></inline-formula> in <inline-formula><tex-math id=\"M3\">begin{document}$ L^{2} $end{document}</tex-math></inline-formula>-sense. The operator <inline-formula><tex-math id=\"M4\">begin{document}$ L $end{document}</tex-math></inline-formula> considered in this paper was first introduced to dissipate the solutions of the wave equation in the paper studied by Charão-Ikehata [<xref ref-type=\"bibr\" rid=\"b7\">7</xref>]. We will discuss the asymptotic property of the solution as time goes to infinity to our Cauchy problem, and in particular, we classify the property of the solutions into three parts from the viewpoint of regularity of the initial data, that is, diffusion-like, wave-like, and both of them.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"254 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79474635","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Lower bounds for Orlicz eigenvalues Orlicz特征值的下界

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-04-15 DOI: 10.3934/dcds.2021158

A. Salort

{"title":"Lower bounds for Orlicz eigenvalues","authors":"A. Salort","doi":"10.3934/dcds.2021158","DOIUrl":"https://doi.org/10.3934/dcds.2021158","url":null,"abstract":"In this article we consider the following weighted nonlinear eigenvalue problem for the <inline-formula><tex-math id=\"M1\">begin{document}$ g- $end{document}</tex-math></inline-formula>Laplacian<disp-formula> <label/> <tex-math id=\"FE1\"> begin{document}$ -{text{ div}}left( g(|nabla u|)frac{nabla u}{|nabla u|}right) = lambda w(x) h(|u|)frac{u}{|u|} quad text{ in }Omegasubset mathbb R^n, ngeq 1 $end{document} </tex-math></disp-formula>with Dirichlet boundary conditions. Here <inline-formula><tex-math id=\"M2\">begin{document}$ w $end{document}</tex-math></inline-formula> is a suitable weight and <inline-formula><tex-math id=\"M3\">begin{document}$ g = G' $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M4\">begin{document}$ h = H' $end{document}</tex-math></inline-formula> are appropriated Young functions satisfying the so called <inline-formula><tex-math id=\"M5\">begin{document}$ Delta' $end{document}</tex-math></inline-formula> condition, which includes for instance logarithmic perturbation of powers and different power behaviors near zero and infinity. We prove several properties on its spectrum, being our main goal to obtain lower bounds of eigenvalues in terms of <inline-formula><tex-math id=\"M6\">begin{document}$ G $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M7\">begin{document}$ H $end{document}</tex-math></inline-formula>, <inline-formula><tex-math id=\"M8\">begin{document}$ w $end{document}</tex-math></inline-formula> and the normalization <inline-formula><tex-math id=\"M9\">begin{document}$ mu $end{document}</tex-math></inline-formula> of the corresponding eigenfunctions.We introduce some new strategies to obtain results that generalize several inequalities from the literature of <inline-formula><tex-math id=\"M10\">begin{document}$ p- $end{document}</tex-math></inline-formula>Laplacian type eigenvalues.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"15 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87791754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 5

Asymptotic spreading for Fisher-KPP reaction-diffusion equations with heterogeneous shifting diffusivity 具有非均相移动扩散系数的Fisher-KPP反应扩散方程的渐近扩散

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-03-29 DOI: 10.3934/dcdss.2021146

Grégory Faye, T. Giletti, Matt Holzer

{"title":"Asymptotic spreading for Fisher-KPP reaction-diffusion equations with heterogeneous shifting diffusivity","authors":"Grégory Faye, T. Giletti, Matt Holzer","doi":"10.3934/dcdss.2021146","DOIUrl":"https://doi.org/10.3934/dcdss.2021146","url":null,"abstract":"We determine the asymptotic spreading speed of the solutions of a Fisher-KPP reaction-diffusion equation, starting from compactly supported initial data, when the diffusion coefficient is a fixed bounded monotone profile that is shifted at a given forcing speed and satisfies a general uniform ellipticity condition. Depending on the monotonicity of the profile, we are able to characterize this spreading speed as a function of the forcing speed and the two linear spreading speeds associated to the asymptotic problems at begin{document}$ x = pm infty $end{document}. Most notably, when the profile of the diffusion coefficient is increasing we show that there is an intermediate range for the forcing speed where spreading actually occurs at a speed which is larger than the linear speed associated with the homogeneous state around the position of the front. We complement our study with the construction of strictly monotone traveling front solutions with strong exponential decay near the unstable state when the profile of the diffusion coefficient is decreasing and in the regime where the forcing speed is precisely the selected spreading speed.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"5 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89816030","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Realizing arbitrary $d$-dimensional dynamics by renormalization of $C^d$-perturbations of identity 通过单位元C^d扰动的重整化实现任意d维动态

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-03-29 DOI: 10.3934/dcds.2021129

B. Fayad, M. Saprykina

引用次数: 1

Recovering the initial condition in the one-phase Stefan problem 恢复单相斯特芬问题的初始条件

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-03-26 DOI: 10.3934/dcdss.2021087

Chifaa Ghanmi, S. Aouadi, Faouzi Triki

引用次数: 2

Sublacunary sets and interpolation sets for nilsequences 零序列的次元集和插值集

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-03-25 DOI: 10.3934/dcds.2021175

Anh N. Le

{"title":"Sublacunary sets and interpolation sets for nilsequences","authors":"Anh N. Le","doi":"10.3934/dcds.2021175","DOIUrl":"https://doi.org/10.3934/dcds.2021175","url":null,"abstract":"A set <inline-formula><tex-math id=\"M1\">begin{document}$ E subset mathbb{N} $end{document}</tex-math></inline-formula> is an interpolation set for nilsequences if every bounded function on <inline-formula><tex-math id=\"M2\">begin{document}$ E $end{document}</tex-math></inline-formula> can be extended to a nilsequence on <inline-formula><tex-math id=\"M3\">begin{document}$ mathbb{N} $end{document}</tex-math></inline-formula>. Following a theorem of Strzelecki, every lacunary set is an interpolation set for nilsequences. We show that sublacunary sets are not interpolation sets for nilsequences. Here <inline-formula><tex-math id=\"M4\">begin{document}$ {r_n: n in mathbb{N}} subset mathbb{N} $end{document}</tex-math></inline-formula> with <inline-formula><tex-math id=\"M5\">begin{document}$ r_1 < r_2 < ldots $end{document}</tex-math></inline-formula> is sublacunary if <inline-formula><tex-math id=\"M6\">begin{document}$ lim_{n to infty} (log r_n)/n = 0 $end{document}</tex-math></inline-formula>. Furthermore, we prove that the union of an interpolation set for nilsequences and a finite set is an interpolation set for nilsequences. Lastly, we provide a new class of interpolation sets for Bohr almost periodic sequences, and as a result, obtain a new example of interpolation set for <inline-formula><tex-math id=\"M7\">begin{document}$ 2 $end{document}</tex-math></inline-formula>-step nilsequences which is not an interpolation set for Bohr almost periodic sequences.","PeriodicalId":11254,"journal":{"name":"Discrete & Continuous Dynamical Systems - S","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89024961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The critical points of the elastic energy among curves pinned at endpoints 曲线间弹性能的临界点固定在端点处

Discrete & Continuous Dynamical Systems - S Pub Date : 2021-03-22 DOI: 10.3934/dcds.2021122

Kensuke Yoshizawa

引用次数: 4