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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
An eigenvalue problem for a variable exponent problem, via topological degree 通过拓扑度，求解变指数问题的特征值问题
3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023134
Raúl Manásevich, Satoshi Tanaka
{"title":"An eigenvalue problem for a variable exponent problem, via topological degree","authors":"Raúl Manásevich, Satoshi Tanaka","doi":"10.3934/dcds.2023134","DOIUrl":"https://doi.org/10.3934/dcds.2023134","url":null,"abstract":"The problem$ begin{equation*} left{ begin{array}{l} -Delta_{p(|x|)} u - Delta_{q} u = lambda (|u|^{p(|x|)-2}u + |u|^{q-2}u) quad mbox{in} mathcal B , u = 0 quad mbox{on} partial mathcal B end{array} right. end{equation*} $is considered, where $ mathcal B = { x in mathbb{R}^N : |x|<R } $, $ N ge 1 $, $ Delta_{p(|x|)} u = mbox{div} (|nabla u|^{p(|x|)-2}nabla u) $, $ p(r) $ is continuous and satisfies $ p(r)>1 $ on $ [0, R] $, $ Delta_{q} u = mbox{div}(|nabla u|^{q-2}nabla u) $, and $ q>1 $. The existence of positive solutions is proved for every $ lambda>lambda_1(q) $, where $ lambda_1(q) $ is the first eigenvalue of $ q $-Laplacian.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"5 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":"135560507","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
Boundary layer problem on the chemotaxis model with Robin boundary conditions 具有Robin边界条件的趋化模型的边界层问题
3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023108
Qianqian Hou
{"title":"Boundary layer problem on the chemotaxis model with Robin boundary conditions","authors":"Qianqian Hou","doi":"10.3934/dcds.2023108","DOIUrl":"https://doi.org/10.3934/dcds.2023108","url":null,"abstract":"This paper is concerned with the boundary layer problem on a chemotaxis system modelling boundary layer formation of aerobic bacteria in fluid. Completing the system with physical Robin-type boundary conditions for oxygen and no-flux boundary conditions for bacteria, we show that the gradients of its radial solutions in a region between two concentric spheres possessing boundary layer effects as the oxygen diffusion rate $ varepsilon $ goes to zero and the boundary-layer thickness is of order $ mathcal{O}(varepsilon^alpha) $ with $ 0<alpha<frac{1}{2} $.","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"249 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":"135700134","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
Robust non-hyperbolic fibred quadratic polynomial dynamics 鲁棒非双曲纤维二次多项式动力学
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023080
Igsyl Domínguez, M. Ponce
{"title":"Robust non-hyperbolic fibred quadratic polynomial dynamics","authors":"Igsyl Domínguez, M. Ponce","doi":"10.3934/dcds.2023080","DOIUrl":"https://doi.org/10.3934/dcds.2023080","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"28 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72769949","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
Sequence complexity, rigidity and logarithmic Sarnak conjecture 序列复杂性、刚性和对数Sarnak猜想
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2022187
Rui Qiu, R. Wei, Leiye Xu
{"title":"Sequence complexity, rigidity and logarithmic Sarnak conjecture","authors":"Rui Qiu, R. Wei, Leiye Xu","doi":"10.3934/dcds.2022187","DOIUrl":"https://doi.org/10.3934/dcds.2022187","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"58 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72876532","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
Normalized solutions for Kirchhoff type equations with combined nonlinearities: The Sobolev critical case 组合非线性Kirchhoff型方程的归一化解:Sobolev临界情况
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023035
Xiaojing Feng, Haidong Liu, Zhitao Zhang
{"title":"Normalized solutions for Kirchhoff type equations with combined nonlinearities: The Sobolev critical case","authors":"Xiaojing Feng, Haidong Liu, Zhitao Zhang","doi":"10.3934/dcds.2023035","DOIUrl":"https://doi.org/10.3934/dcds.2023035","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":"84313208","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: 2
Global dynamics of evolution systems with asymptotic annihilation 渐近湮灭演化系统的全局动力学
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023025
Taishan Yi, Xiao-Qiang Zhao
{"title":"Global dynamics of evolution systems with asymptotic annihilation","authors":"Taishan Yi, Xiao-Qiang Zhao","doi":"10.3934/dcds.2023025","DOIUrl":"https://doi.org/10.3934/dcds.2023025","url":null,"abstract":"","PeriodicalId":51007,"journal":{"name":"Discrete and Continuous Dynamical Systems","volume":"46 1","pages":""},"PeriodicalIF":1.1,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77252085","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: 2
Emergence of large densities in a chemotaxis system with signaling loops, nonlinear signal productions and competitions sources under nonradial symmetry case 非径向对称条件下具有信号回路、非线性信号产生和竞争源的趋化系统中大密度的出现
IF 1.1 3区 数学
Discrete and Continuous Dynamical Systems Pub Date : 2023-01-01 DOI: 10.3934/dcds.2023090
Guangyu Xu
{"title":"Emergence of large densities in a chemotaxis system with signaling loops, nonlinear signal productions and competitions sources under nonradial symmetry case","authors":"Guangyu Xu","doi":"10.3934/dcds.2023090","DOIUrl":"https://doi.org/10.3934/dcds.2023090","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":"73736858","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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