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Multi-peak solutions for logarithmic Schrödinger equations with potentials unbounded below 以下电位无界的对数Schrödinger方程的多峰解
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023073
Xiaoming An, Xian-lin Yang
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引用次数: 0
Modified scattering for the nonlinear nonlocal Schrödinger equation in two space dimensions 二维非线性非局部Schrödinger方程的修正散射
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023065
N. Hayashi, P. Naumkin
{"title":"Modified scattering for the nonlinear nonlocal Schrödinger equation in two space dimensions","authors":"N. Hayashi, P. Naumkin","doi":"10.3934/dcds.2023065","DOIUrl":"https://doi.org/10.3934/dcds.2023065","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"54 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79264726","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}
引用次数: 0
Bistable pulsating wave of a competition model in rapidly varying media and its homogenization limit 快速变化介质中竞争模型的双稳脉动波及其均匀化极限
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023012
Weiwei Ding, Rui Huang, Xiao Yu
{"title":"Bistable pulsating wave of a competition model in rapidly varying media and its homogenization limit","authors":"Weiwei Ding, Rui Huang, Xiao Yu","doi":"10.3934/dcds.2023012","DOIUrl":"https://doi.org/10.3934/dcds.2023012","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"12 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77959575","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}
引用次数: 1
Vacuum and singularity formation for compressible Euler equations with time-dependent damping 具有时变阻尼的可压缩欧拉方程的真空和奇点形成
3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2022184
Ying Sui, Weiqiang Wang, Huimin Yu
{"title":"Vacuum and singularity formation for compressible Euler equations with time-dependent damping","authors":"Ying Sui, Weiqiang Wang, Huimin Yu","doi":"10.3934/dcds.2022184","DOIUrl":"https://doi.org/10.3934/dcds.2022184","url":null,"abstract":"In this paper, vacuum and singularity formation are considered for compressible Euler equations with time-dependent damping. For $ 1<gamma{leq} 3 $, by constructing some new control functions ingeniously, we obtain the lower bounds estimates on density for arbitrary classical solutions. Basing on these lower estimates, we succeed in proving the singular formation theorem for all $ lambda $, which was open in [19] for some cases. Moreover, the singularity formation of the compressible Euler equations when $ gamma = 3 $ is investigated, too.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"16 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":"134996609","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}
引用次数: 1
Refined spike profiles of constraint minimizers for the planar Schrödinger-Poisson system with logarithmic potentials 具有对数电位的平面Schrödinger-Poisson系统约束最小化器的精细尖峰剖面
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023100
Yujin Guo, Wenning Liang, Yan Li
{"title":"Refined spike profiles of constraint minimizers for the planar Schrödinger-Poisson system with logarithmic potentials","authors":"Yujin Guo, Wenning Liang, Yan Li","doi":"10.3934/dcds.2023100","DOIUrl":"https://doi.org/10.3934/dcds.2023100","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"131 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74986822","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}
引用次数: 0
Spatial dynamics of a nonlocal dispersal Leslie-Gower predator-prey model with some shifting habitats 具有迁移生境的非局部扩散Leslie-Gower捕食-猎物模型的空间动力学
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023037
Qinhe Fang, Hongmei Cheng, Rong Yuan
{"title":"Spatial dynamics of a nonlocal dispersal Leslie-Gower predator-prey model with some shifting habitats","authors":"Qinhe Fang, Hongmei Cheng, Rong Yuan","doi":"10.3934/dcds.2023037","DOIUrl":"https://doi.org/10.3934/dcds.2023037","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":"76720267","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}
引用次数: 0
Boundedness of semilinear Duffing equations with Liouvillean frequency 具有liouville频率的半线性Duffing方程的有界性
3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023127
Min Li, Xiong Li
{"title":"Boundedness of semilinear Duffing equations with Liouvillean frequency","authors":"Min Li, Xiong Li","doi":"10.3934/dcds.2023127","DOIUrl":"https://doi.org/10.3934/dcds.2023127","url":null,"abstract":"We are concerned with the quasi-periodic semilinear Duffing equation $ x''+omega^2x+g(x,t) = 0, $ where $ omega $ is a Diophantine number, $ g(x,t) $ is bounded, real analytic in $ x $ and $ t $, and is quasi-periodic in $ t $ with the frequency $ tilde{omega} = (1, alpha) $, where $ alpha $ is Liouvillean. Without assuming the twist condition and the polynomial-like condition on this equation, we will prove the boundedness of all solutions.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"51 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":"135319485","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}
引用次数: 0
A Liouville theorem for the Chern–Simons–Schrödinger equation Chern-Simons-Schrödinger方程的刘维尔定理
3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023110
Benjamin Dodson
{"title":"A Liouville theorem for the Chern–Simons–Schrödinger equation","authors":"Benjamin Dodson","doi":"10.3934/dcds.2023110","DOIUrl":"https://doi.org/10.3934/dcds.2023110","url":null,"abstract":"In this paper we prove a Liouville theorem for the Chern–Simons–Schrödinger equation. This result is consistent with the soliton resolution conjecture for initial data that does not lie in a weighted space. See [10] for the soliton resolution result in a weighted space.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"41 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":"135839031","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}
引用次数: 1
Linearization of a nonautonomous unbounded system with hyperbolic linear part: A spectral approach 具有双曲线性部分的非自治无界系统的线性化:谱方法
3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023112
Mengda Wu, Yonghui Xia
{"title":"Linearization of a nonautonomous unbounded system with hyperbolic linear part: A spectral approach","authors":"Mengda Wu, Yonghui Xia","doi":"10.3934/dcds.2023112","DOIUrl":"https://doi.org/10.3934/dcds.2023112","url":null,"abstract":"Palmer's linearization theorem states that a hyperbolic linear system is topologically conjugated to its bounded perturbation. Recently, Huerta (DCDS 2020 [8]), Castañeda and Robledo (DCDS 2018 [3]) and Lin (NA 2007 [13]) generalized Palmer's theorem to the linearization with unbounded perturbation (continuous or discrete) by assuming that the linear part of the system is contractive or nonuniformly contractive. However, these previous works sacrifice the hyperbolicity of the linear part. Is it possible to study the linearization with unbounded perturbations in the hyperbolic case? In this paper, we improve the previous works [3,8,13] to the hyperbolic unbounded systems. For the contraction, each trajectory crosses its respective unit sphere exactly once. However, for the hyperbolic system, either the trajectory does not cross the unit sphere, or the trajectory cross it twice. Thus, the standard method used in the previous works for the contractive case is not valid for the hyperbolic case yet. We develop a method to overcome the difficulty based on two 'cylinders'. Furthermore, quantitative results for the parameters are provided.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"68 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":"136256735","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}
引用次数: 0
Global and exponential stabilization of morphogenesis models with logarithmic sensitivity and linear degradation 具有对数灵敏度和线性退化的形态发生模型的全局和指数镇定
3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023115
Lin Chen, Fanze Kong, Qi Wang
{"title":"Global and exponential stabilization of morphogenesis models with logarithmic sensitivity and linear degradation","authors":"Lin Chen, Fanze Kong, Qi Wang","doi":"10.3934/dcds.2023115","DOIUrl":"https://doi.org/10.3934/dcds.2023115","url":null,"abstract":"We study a coupled PDE system describing the dynamics of morphogen transport in epithelia, where the morphogens sense the spatial gradient of the logarithm of the signal following the empirically well-tested Webner–Fecher law. We prove that this fully parabolic system is globally well-posed and its unique solution is classical and uniformly bounded in time. Moreover, we find that regardless of the strength of the chemotactic motion and the size of the initial data, a linear degradation is strong enough to overcome the logarithmic singularity and destabilize the system globally and exponentially in time. Several numerical simulations are presented to illustrate and support the theoretical results.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"50 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":"136366912","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}
引用次数: 0
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