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Propagation dynamics of a nonlocal reaction-diffusion system 非局部反应扩散系统的传播动力学
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023028
B. Han, D. Kong
{"title":"Propagation dynamics of a nonlocal reaction-diffusion system","authors":"B. Han, D. Kong","doi":"10.3934/dcds.2023028","DOIUrl":"https://doi.org/10.3934/dcds.2023028","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":" 24","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72379345","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
Global existence and blow-up of solutions to the double nonlinear porous medium equation 双非线性多孔介质方程解的整体存在性和爆破性
3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023124
Bolys Sabitbek, Berikbol T. Torebek
{"title":"Global existence and blow-up of solutions to the double nonlinear porous medium equation","authors":"Bolys Sabitbek, Berikbol T. Torebek","doi":"10.3934/dcds.2023124","DOIUrl":"https://doi.org/10.3934/dcds.2023124","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"66 12 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":"134980900","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
Generalized focal points and local Sturmian theory for linear Hamiltonian systems 线性哈密顿系统的广义焦点与局部Sturmian理论
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023082
Peter Šepitka, R. Hilscher
{"title":"Generalized focal points and local Sturmian theory for linear Hamiltonian systems","authors":"Peter Šepitka, R. Hilscher","doi":"10.3934/dcds.2023082","DOIUrl":"https://doi.org/10.3934/dcds.2023082","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"14 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83037395","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
Nonlinear stability of elliptic equilibria in Hamiltonian systems with resonances of order four with interactions 带相互作用的四阶共振哈密顿系统椭圆平衡的非线性稳定性
3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023119
Claudio Sierpe, Claudio Vidal
{"title":"Nonlinear stability of elliptic equilibria in Hamiltonian systems with resonances of order four with interactions","authors":"Claudio Sierpe, Claudio Vidal","doi":"10.3934/dcds.2023119","DOIUrl":"https://doi.org/10.3934/dcds.2023119","url":null,"abstract":"In this paper, we advance the study of the Lyapunov stability and instability of equilibrium solutions of Hamiltonian flows, which is one of the oldest problems in mathematical physics. More precisely, in this work we study the nonlinear stability in the Lyapunov sense of one equilibrium solution in autonomous Hamiltonian systems with $ n $-degrees of freedom, assuming the existence of two vectors of resonance, both of order four, with interaction in one frequency. We provide conditions to obtain a type of formal stability, called Lie stability. Subsequently, we guarantee some sufficient conditions to obtain exponential stability in the sense of Nekhoroshev for Lie stable systems with three and four degrees of freedom. In addition, we give sufficient conditions for the instability in the sense of Lyapunov. We apply some of our results in the spatial satellite problem at one of its equilibrium points, which is a novelty in this problem.","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":"135057376","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
Long-time approximations of small-amplitude, long-wavelength FPUT solutions 长时间近似的小振幅，长波长FPUT解决方案
3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023131
Trevor Norton, C. Eugene Wayne
{"title":"Long-time approximations of small-amplitude, long-wavelength FPUT solutions","authors":"Trevor Norton, C. Eugene Wayne","doi":"10.3934/dcds.2023131","DOIUrl":"https://doi.org/10.3934/dcds.2023131","url":null,"abstract":"It is well known that the Korteweg-de Vries (KdV) equation and its generalizations serve as modulation equations for traveling wave solutions to generic Fermi-Pasta-Ulam-Tsingou (FPUT) lattices. Explicit approximation estimates and other such results have been proved in this case. However, situations in which the defocusing modified KdV (mKdV) equation is expected to be the modulation equation have been much less studied. As seen in numerical experiments, the kink solution of the mKdV seems essential in understanding the $beta$-FPUT recurrence. In this paper, we derive explicit approximation results for solutions of the FPUT using the mKdV as a modulation equation. In contrast to previous work, our estimates allow for solutions to be non-localized as to allow approximate kink solutions. These results allow us to conclude meta-stability results of kink-like solutions of the FPUT.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"25 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":"135319260","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
Standing waves with prescribed norm for the coupled Hartree-Fock system 耦合Hartree-Fock系统的定范数驻波
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023043
Xiaoyutao Luo, Vicentiu D. Rădulescu, Maoding Zhen
{"title":"Standing waves with prescribed norm for the coupled Hartree-Fock system","authors":"Xiaoyutao Luo, Vicentiu D. Rădulescu, Maoding Zhen","doi":"10.3934/dcds.2023043","DOIUrl":"https://doi.org/10.3934/dcds.2023043","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"49 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90925256","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
The center problem on piecewise smooth differential systems with two zones 两区域分段光滑微分系统的中心问题
3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023113
Changwu Zou, Guangfeng Dong, Changjian Liu, Jiazhong Yang
{"title":"The center problem on piecewise smooth differential systems with two zones","authors":"Changwu Zou, Guangfeng Dong, Changjian Liu, Jiazhong Yang","doi":"10.3934/dcds.2023113","DOIUrl":"https://doi.org/10.3934/dcds.2023113","url":null,"abstract":"In this paper we shall study $ Sigma $-center problem on piecewise smooth systems with two zones divided by a straight line in the real plane. We first give some necessary and sufficient conditions for the crossing $ Sigma $-center by taking advantage of the forms of the first integrals. Then for applications, we completely describe the $ Sigma $-centers from both the algebra and geometry points of view when the both of two sub-systems are linear.","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":"136256740","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
Best constants and existence of maximizers for anisotropic weighted Moser-Trudinger inequalities in $ mathbb{R}^{N} $ $ mathbb{R}^{N} $中各向异性加权Moser-Trudinger不等式的最佳常数和最大值存在性
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023052
Tingzhi Cheng, Tao Zhang, Chunqin Zhou
{"title":"Best constants and existence of maximizers for anisotropic weighted Moser-Trudinger inequalities in $ mathbb{R}^{N} $","authors":"Tingzhi Cheng, Tao Zhang, Chunqin Zhou","doi":"10.3934/dcds.2023052","DOIUrl":"https://doi.org/10.3934/dcds.2023052","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"63 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89071175","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
Phase transition for the McKean-Vlasov equation of weakly coupled Hodgkin-Huxley oscillators 弱耦合霍奇金-赫胥黎振子McKean-Vlasov方程的相变
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023081
J. Vukadinovic
{"title":"Phase transition for the McKean-Vlasov equation of weakly coupled Hodgkin-Huxley oscillators","authors":"J. Vukadinovic","doi":"10.3934/dcds.2023081","DOIUrl":"https://doi.org/10.3934/dcds.2023081","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"1 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89439071","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
Square function estimates for the evolutionary p-Laplace equation 进化p-拉普拉斯方程的平方函数估计
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023044
K. Nyström
{"title":"Square function estimates for the evolutionary p-Laplace equation","authors":"K. Nyström","doi":"10.3934/dcds.2023044","DOIUrl":"https://doi.org/10.3934/dcds.2023044","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":"90507076","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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