{"title":"Large-time behavior of solutions for unipolar Euler-Poisson equations with critical over-damping","authors":"Jianing Xu, Ming Mei, Hai-liang Li","doi":"10.3934/dcds.2023092","DOIUrl":"https://doi.org/10.3934/dcds.2023092","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"36 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81353140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Vortex states of Bose-Einstein condensates with attractive interactions","authors":"Tingxi Hu, Lu Lu","doi":"10.3934/dcds.2023003","DOIUrl":"https://doi.org/10.3934/dcds.2023003","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"51 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88502100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Some further progress for boundedness of solutions to a quasilinear higher–dimensional chemotaxis–haptotaxis model with nonlinear diffusion","authors":"Jiashan Zheng, Jianing Xie","doi":"10.3934/dcds.2023095","DOIUrl":"https://doi.org/10.3934/dcds.2023095","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"24 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91025532","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present the topological transitivity of a class of diffeomorphisms on the thickened torus, including the partially hyperbolic example introduced by Ittai Kan in 1994, which is well known for the first systems with the intermingled basins phenomenon.
{"title":"Topological transitivity of Kan-type partially hyperbolic diffeomorphisms","authors":"Mingyang Xia","doi":"10.3934/dcds.2023117","DOIUrl":"https://doi.org/10.3934/dcds.2023117","url":null,"abstract":"We present the topological transitivity of a class of diffeomorphisms on the thickened torus, including the partially hyperbolic example introduced by Ittai Kan in 1994, which is well known for the first systems with the intermingled basins phenomenon.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"238 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136306365","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Hausdorff dimension analysis of sets with the product of consecutive vs single partial quotients in continued fractions","authors":"Mumtaz Hussain, Bixuan Li, N. Shulga","doi":"10.3934/dcds.2023099","DOIUrl":"https://doi.org/10.3934/dcds.2023099","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"8 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74925351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the present work we study the existence and non-existence of nonnegative solutions to a class of deterministic KPZ system with nonlocal gradient term. More precisely we will consider the system$ begin{equation*} left{ begin{array}{rcll} (-Delta)^{s} u & = &|mathbb{D}_{s} v|^q + rho f,, & quad {rm{in }}; Omega, (-Delta)^{s} v & = & |mathbb{D}_{s} u|^p + tau g,, & quad {rm{in }}; Omega, u = v& = & 0 &quad {text{in }} mathbb{R}^N setminus Omega end{array} right. end{equation*} $where $ Omega $ is a bounded regular ($ C^2 $) domain of $ mathbb{R}^N $ and $ p, qge 1 $. $ f,g $ are nonnegative measurable functions satisfying some additional hypotheses and $ rho, tau ge 0 $.Here $ mathbb{D}_{s} $ represents a nonlocal 'gradient term' that will be specified below. In some particular cases, we are able to show the optimality of the condition imposed on the data $ f,g $ and $ rho,tau $.
{"title":"Fractional KPZ system with nonlocal \"gradient terms\"","authors":"Abdelbadie Younes, Kheireddine Biroud, Fethi Mahmoudi, Boumediene Abdellaoui","doi":"10.3934/dcds.2023106","DOIUrl":"https://doi.org/10.3934/dcds.2023106","url":null,"abstract":"In the present work we study the existence and non-existence of nonnegative solutions to a class of deterministic KPZ system with nonlocal gradient term. More precisely we will consider the system$ begin{equation*} left{ begin{array}{rcll} (-Delta)^{s} u & = &|mathbb{D}_{s} v|^q + rho f,, & quad {rm{in }}; Omega, (-Delta)^{s} v & = & |mathbb{D}_{s} u|^p + tau g,, & quad {rm{in }}; Omega, u = v& = & 0 &quad {text{in }} mathbb{R}^N setminus Omega end{array} right. end{equation*} $where $ Omega $ is a bounded regular ($ C^2 $) domain of $ mathbb{R}^N $ and $ p, qge 1 $. $ f,g $ are nonnegative measurable functions satisfying some additional hypotheses and $ rho, tau ge 0 $.Here $ mathbb{D}_{s} $ represents a nonlocal 'gradient term' that will be specified below. In some particular cases, we are able to show the optimality of the condition imposed on the data $ f,g $ and $ rho,tau $.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135556556","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Systems of Stieltjes differential equations and application to a predator-prey model of an exploited fishery","authors":"Lamiae Maia, N. El Khattabi, M. Frigon","doi":"10.3934/dcds.2023086","DOIUrl":"https://doi.org/10.3934/dcds.2023086","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"11 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82604430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Corrigendum and Addendum to : \"SINGULAR weighted sharp trudinger-moser inequalities defined on $ mathbb{R}^N $ and applications to elliptic nonlinear equations\" DOI: 10.3934/dcds.2021137","authors":"S. Aouaoui, Rahma Jlel","doi":"10.3934/dcds.2023053","DOIUrl":"https://doi.org/10.3934/dcds.2023053","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"143 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88567727","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Livšic theorem asserts that, for Anosov diffeomorphisms, a Lipschitz observable is a coboundary if all its Birkhoff sums on every periodic orbits are equal to zero. The transfer function is then Lipschitz. We prove a positive Livšic theorem which asserts that a Lipschitz observable is bounded from below by a coboundary if and only if all its Birkhoff sums on periodic orbits are non negative. The new result is that the coboundary can be chosen Lipschitz with a uniform control on the Lipschitz norm. In addition our result holds true for possibly non invertible and not transitive $ C^1 $ maps. We actually prove the main result in the setting of locally maximal hyperbolic sets for general $ C^1 $ map. The construction of the coboundary uses a new notion of the Lax-Oleinik operator that is a standard tool in the discrete Aubry-Mather theory.
{"title":"Lipschitz sub-actions for locally maximal hyperbolic sets of a $ C^1 $ map","authors":"Xifeng Su, Philippe Thieullen, Wenzhe Yu","doi":"10.3934/dcds.2023120","DOIUrl":"https://doi.org/10.3934/dcds.2023120","url":null,"abstract":"Livšic theorem asserts that, for Anosov diffeomorphisms, a Lipschitz observable is a coboundary if all its Birkhoff sums on every periodic orbits are equal to zero. The transfer function is then Lipschitz. We prove a positive Livšic theorem which asserts that a Lipschitz observable is bounded from below by a coboundary if and only if all its Birkhoff sums on periodic orbits are non negative. The new result is that the coboundary can be chosen Lipschitz with a uniform control on the Lipschitz norm. In addition our result holds true for possibly non invertible and not transitive $ C^1 $ maps. We actually prove the main result in the setting of locally maximal hyperbolic sets for general $ C^1 $ map. The construction of the coboundary uses a new notion of the Lax-Oleinik operator that is a standard tool in the discrete Aubry-Mather theory.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135052330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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