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Discrete and Continuous Dynamical Systems-Series S最新文献

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Heat equations with fast convection: Source-type solutions and large-time behaviour 具有快速对流的热方程:源型解和大时间行为
4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023182
Jørgen Endal, Liviu I. Ignat, Fernando Quirós
{"title":"Heat equations with fast convection: Source-type solutions and large-time behaviour","authors":"Jørgen Endal, Liviu I. Ignat, Fernando Quirós","doi":"10.3934/dcdss.2023182","DOIUrl":"https://doi.org/10.3934/dcdss.2023182","url":null,"abstract":"We study the existence and uniqueness of source-type solutions to the Cauchy problem for the heat equation with fast convection under certain tail control assumptions. We allow the solutions to change sign, but we will in fact show that they have the same sign as the initial data, which is a multiple of the Dirac delta. As an application, we obtain the large-time behaviour of nonnegative bounded solutions with integrable initial data to heat equations with fast convection, covering the case of several dimensions that remained open since the end of last century.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136053645","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Blowup phenomena for a fourth order wave equation at high initial energy level 高初始能级四阶波动方程的爆破现象
4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023178
Tiantian Pang, Lanlan Qin, Xingchang Wang
{"title":"Blowup phenomena for a fourth order wave equation at high initial energy level","authors":"Tiantian Pang, Lanlan Qin, Xingchang Wang","doi":"10.3934/dcdss.2023178","DOIUrl":"https://doi.org/10.3934/dcdss.2023178","url":null,"abstract":"This paper deals with the initial boundary value problem of a class of fourth order wave equations with nonlinear strain and linear weak damping terms. By establishing the invariance of the unstable set and a delicate auxiliary function, we give a sufficient condition such that the solution blows up in a finite time at high initial energy level.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135700153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Learning nonlocal weights for second-order nonlocal super-resolution 二阶非局部超分辨率的非局部权值学习
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023155
A. Laghrib, F. A. Bella, M. Nachaoui, M. Hakim
{"title":"Learning nonlocal weights for second-order nonlocal super-resolution","authors":"A. Laghrib, F. A. Bella, M. Nachaoui, M. Hakim","doi":"10.3934/dcdss.2023155","DOIUrl":"https://doi.org/10.3934/dcdss.2023155","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86154957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Large and moderate deviation principles for path-distribution-dependent stochastic differential equations 路径分布相关随机微分方程的大、中偏差原理
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023015
Xinyi Gu, Yulin Song
{"title":"Large and moderate deviation principles for path-distribution-dependent stochastic differential equations","authors":"Xinyi Gu, Yulin Song","doi":"10.3934/dcdss.2023015","DOIUrl":"https://doi.org/10.3934/dcdss.2023015","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83577763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Pattern formation of Brusselator in the reaction-diffusion system 反应扩散体系中Brusselator模式的形成
4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2022103
Yansu Ji, Jianwei Shen, Xiaochen Mao
{"title":"Pattern formation of Brusselator in the reaction-diffusion system","authors":"Yansu Ji, Jianwei Shen, Xiaochen Mao","doi":"10.3934/dcdss.2022103","DOIUrl":"https://doi.org/10.3934/dcdss.2022103","url":null,"abstract":"Time delay profoundly impacts reaction-diffusion systems, which has been considered in many areas, especially infectious diseases, neurodynamics, and chemistry. This paper aims to investigate the pattern dynamics of the reaction-diffusion model with time delay. We obtain the condition in which the system induced the Hopf bifurcation and Turing instability as the parameter of the diffusion term and time delay changed. Meanwhile, the amplitude equation of the reaction-diffusion system with time delay is also derived based on the Friedholm solvability condition and the multi-scale analysis method near the critical point of phase transition. We discussed the stability of the amplitude equation. Theoretical results demonstrate that the delay can induce rich pattern dynamics in the Brusselator reaction-diffusion system, such as strip and hexagonal patterns. It is evident that time delay causes steady-state changes in the spatial pattern under certain conditions but does not cause changes in pattern selection under certain conditions. However, diffusion and delayed feedback affect pattern formation and pattern selection. This paper provides a feasible method to study reaction-diffusion systems with time delay and the development of the amplitude equation. The numerical simulation well verifies and supports the theoretical results.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136297049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Large deviation principle for distribution dependent S(P)DEs with singular drift 奇异漂移分布相关S(P)DEs的大偏差原理
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023028
Yongqiang Suo
{"title":"Large deviation principle for distribution dependent S(P)DEs with singular drift","authors":"Yongqiang Suo","doi":"10.3934/dcdss.2023028","DOIUrl":"https://doi.org/10.3934/dcdss.2023028","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73465327","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Moore-Gibson-Thompson equation with thermal effects of Gurtin-Pipkin type 具有Gurtin-Pipkin型热效应的Moore-Gibson-Thompson方程
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023051
Filippo Dell’Oro, V. Pata
{"title":"On the Moore-Gibson-Thompson equation with thermal effects of Gurtin-Pipkin type","authors":"Filippo Dell’Oro, V. Pata","doi":"10.3934/dcdss.2023051","DOIUrl":"https://doi.org/10.3934/dcdss.2023051","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73198017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Nodal solutions for critical Robin double phase problems with variable exponent 变指数Robin临界双相问题的节点解
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023095
F. Vetro, Patrick Winkert
{"title":"Nodal solutions for critical Robin double phase problems with variable exponent","authors":"F. Vetro, Patrick Winkert","doi":"10.3934/dcdss.2023095","DOIUrl":"https://doi.org/10.3934/dcdss.2023095","url":null,"abstract":". In this paper, we study a nonlinear double phase problem with variable exponent and critical growth on the boundary. The problem has in the reaction the combined effects of a Carath´eodory perturbation defined only locally and of a critical term. The presence of the critical term does not permit to apply results of the critical point theory to the corresponding energy functional. Thus, we use appropriate cut-off functions and truncation techniques to work on an auxiliary coercive problem. In this way, we can use variational tools to get a sequence of sign changing solutions to our main problem. Further, we show that such a sequence converges to 0 in L ∞ and in the Musielak-Orlicz Sobolev space.","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72404105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 and uniqueness of random nonlocal differential equations with colored noise 带有色噪声的随机非局部微分方程的存在唯一性
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023143
Ruonan Liu
{"title":"Existence and uniqueness of random nonlocal differential equations with colored noise","authors":"Ruonan Liu","doi":"10.3934/dcdss.2023143","DOIUrl":"https://doi.org/10.3934/dcdss.2023143","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78525731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 two solutions for Kirchhoff-double phase problems with a small perturbation without (AR)-condition 无(AR)条件的小扰动双相kirchhoff问题两个解的存在性
IF 1.8 4区 数学
Discrete and Continuous Dynamical Systems-Series S Pub Date : 2023-01-01 DOI: 10.3934/dcdss.2023085
Mahmoud El Ahmadi, M. Berrajaa, A. Ayoujil
{"title":"Existence of two solutions for Kirchhoff-double phase problems with a small perturbation without (AR)-condition","authors":"Mahmoud El Ahmadi, M. Berrajaa, A. Ayoujil","doi":"10.3934/dcdss.2023085","DOIUrl":"https://doi.org/10.3934/dcdss.2023085","url":null,"abstract":"","PeriodicalId":48838,"journal":{"name":"Discrete and Continuous Dynamical Systems-Series S","volume":null,"pages":null},"PeriodicalIF":1.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74245354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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