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Communications on Pure and Applied Analysis最新文献

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Viscous shocks and long-time behavior of scalar conservation laws 粘性冲击与标量守恒律的长时间行为
3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023119
Thierry Gallay, Arnd Scheel
{"title":"Viscous shocks and long-time behavior of scalar conservation laws","authors":"Thierry Gallay, Arnd Scheel","doi":"10.3934/cpaa.2023119","DOIUrl":"https://doi.org/10.3934/cpaa.2023119","url":null,"abstract":"We study the long-time behavior of scalar viscous conservation laws via the structure of $ omega $-limit sets. We show that $ omega $-limit sets always contain constants or shocks by establishing convergence to shocks for arbitrary monotone initial data. In the particular case of Burgers' equation, we review and refine results that parametrize entire solutions in terms of probability measures, and we construct initial data for which the $ omega $-limit set is not reduced to the translates of a single shock. Finally we propose several open problems related to the description of long-time dynamics.","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":"27 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":"135612093","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
Hopf bifurcation in a two-species reaction-diffusion-advection competitive model with nonlocal delay 具有非局部延迟的两种反应-扩散-平流竞争模型的Hopf分岔
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023036
Tingting Wen, Xiaoli Wang, Guohong Zhang
{"title":"Hopf bifurcation in a two-species reaction-diffusion-advection competitive model with nonlocal delay","authors":"Tingting Wen, Xiaoli Wang, Guohong Zhang","doi":"10.3934/cpaa.2023036","DOIUrl":"https://doi.org/10.3934/cpaa.2023036","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221177","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
Infinitely many large energy solutions to a class of nonlocal discrete elliptic boundary value problems 一类非局部离散椭圆型边值问题的无穷多个大能量解
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023037
Y. Long, Qinqin Zhang
{"title":"Infinitely many large energy solutions to a class of nonlocal discrete elliptic boundary value problems","authors":"Y. Long, Qinqin Zhang","doi":"10.3934/cpaa.2023037","DOIUrl":"https://doi.org/10.3934/cpaa.2023037","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221217","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: 3
A remark on the local uniqueness by the monotonicity based method for the magnetic Schrödinger equation 基于单调性方法的磁性Schrödinger方程局部唯一性的注解
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023077
Ryusei Yamashita
{"title":"A remark on the local uniqueness by the monotonicity based method for the magnetic Schrödinger equation","authors":"Ryusei Yamashita","doi":"10.3934/cpaa.2023077","DOIUrl":"https://doi.org/10.3934/cpaa.2023077","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221303","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
Symmetry and monotonicity of positive solutions to systems involving general pseudo-relativistic operators 含广义伪相对论算子系统正解的对称性和单调性
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023045
Xueying Chen, Guanfeng Li
{"title":"Symmetry and monotonicity of positive solutions to systems involving general pseudo-relativistic operators","authors":"Xueying Chen, Guanfeng Li","doi":"10.3934/cpaa.2023045","DOIUrl":"https://doi.org/10.3934/cpaa.2023045","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221345","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
Existence of positive solutions to critical Schrödinger system with mixed interactions in $ {mathbb R}^3 $ {mathbb R}^3 $中具有混合交互作用的临界Schrödinger系统正解的存在性
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023097
Song You, Houwang Li
{"title":"Existence of positive solutions to critical Schrödinger system with mixed interactions in $ {mathbb R}^3 $","authors":"Song You, Houwang Li","doi":"10.3934/cpaa.2023097","DOIUrl":"https://doi.org/10.3934/cpaa.2023097","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":"478 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221766","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
On the synchronization of discrete-time Kuramoto model with frustration 带挫折的离散时间Kuramoto模型的同步问题
3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023109
Tingting Zhu
{"title":"On the synchronization of discrete-time Kuramoto model with frustration","authors":"Tingting Zhu","doi":"10.3934/cpaa.2023109","DOIUrl":"https://doi.org/10.3934/cpaa.2023109","url":null,"abstract":"In this paper, we study the emergent discrete-time dynamics of the Kuramoto model with frustration. For the discrete identical Kuramoto model with frustration, we present the exponential synchronization estimate for some admissible classes of initial configuration confined in a half circle. For the nonidentical oscillators, we exploit the second-order lifting of the original Kuramoto model with frustration and study the emergent behaviors of the corresponding discrete augmented model. More precisely, under a sufficient framework in terms of large coupling strength and small step size, we derive that the initial configuration distributed in a small set of a quarter circle will converge to frequency synchronization.","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":"36 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":"135700499","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
On the Lyapunov exponent for some quasi-periodic cocycles with large parameter 一类大参数拟周期环的Lyapunov指数
3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023102
Bowen Ding, Jinhao Liang
{"title":"On the Lyapunov exponent for some quasi-periodic cocycles with large parameter","authors":"Bowen Ding, Jinhao Liang","doi":"10.3934/cpaa.2023102","DOIUrl":"https://doi.org/10.3934/cpaa.2023102","url":null,"abstract":"Lyapunov exponent plays an important role in the dynamics of quasi-periodic cocycles, and admits an asymptotic formula for Schrödinger cocycle with large parameter (see [12] for analytic case, and see [15] for finitely smooth case). In this paper, we establish similar asymptotic formulas of Lyapunov exponent for two classes of important quasi-periodic cocycles: Szegő cocycles and Schrödinger Mosaic cocycles.","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":"254 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":"135496200","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 dynamics of a two-species competition model in advective homogeneous environments 平流均匀环境中两物种竞争模型的全局动力学
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023021
Jinyu Wei, Bin Liu
{"title":"Global dynamics of a two-species competition model in advective homogeneous environments","authors":"Jinyu Wei, Bin Liu","doi":"10.3934/cpaa.2023021","DOIUrl":"https://doi.org/10.3934/cpaa.2023021","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":"1 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221118","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 Reaction-Diffusion Epidemic Model in Time-Space Periodic Habitat 时空周期生境中非局部反应-扩散流行病模型的空间动力学
IF 1 3区 数学
Communications on Pure and Applied Analysis Pub Date : 2023-01-01 DOI: 10.3934/cpaa.2023072
Ming-Zhen Xin, Bin-Guo Wang
{"title":"Spatial Dynamics of a Nonlocal Reaction-Diffusion Epidemic Model in Time-Space Periodic Habitat","authors":"Ming-Zhen Xin, Bin-Guo Wang","doi":"10.3934/cpaa.2023072","DOIUrl":"https://doi.org/10.3934/cpaa.2023072","url":null,"abstract":"","PeriodicalId":10643,"journal":{"name":"Communications on Pure and Applied Analysis","volume":"36 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70221252","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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