Pub Date : 2023-01-01DOI: 10.4310/cms.2023.v21.n3.a6
Renhai Wang, B. Guo, Chunxiao Guo
{"title":"Well-posedness and long-time dynamics of fractional nonclassical diffusion equations with locally Lipschitz noise","authors":"Renhai Wang, B. Guo, Chunxiao Guo","doi":"10.4310/cms.2023.v21.n3.a6","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n3.a6","url":null,"abstract":"","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","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":"70421921","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}
Pub Date : 2023-01-01DOI: 10.4310/cms.2023.v21.n4.a3
Brock C. Price, Xiangsheng Xu
{"title":"Existence theorems for a fourth-order exponential PDE related to crystal surface relaxation","authors":"Brock C. Price, Xiangsheng Xu","doi":"10.4310/cms.2023.v21.n4.a3","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n4.a3","url":null,"abstract":"","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","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":"70421981","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}
Pub Date : 2023-01-01DOI: 10.4310/cms.2023.v21.n5.a10
Chunxiang Zhao, Chunyan Zhao, C. Zhong
{"title":"Existence of polynomial attractor for a class of extensible beams with nonlocal weak damping","authors":"Chunxiang Zhao, Chunyan Zhao, C. Zhong","doi":"10.4310/cms.2023.v21.n5.a10","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n5.a10","url":null,"abstract":"","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","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":"70422077","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}
Pub Date : 2023-01-01DOI: 10.4310/cms.2023.v21.n5.a11
Bo You
{"title":"Pullback exponential attractors for the three dimensional non-autonomous primitive equations of large scale ocean and atmosphere dynamics","authors":"Bo You","doi":"10.4310/cms.2023.v21.n5.a11","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n5.a11","url":null,"abstract":"","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","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":"70422127","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}
Pub Date : 2023-01-01DOI: 10.4310/cms.2023.v21.n5.a8
Yichen Dai, Zhong Tan, Jiahong Wu
{"title":"A class of global large solutions to the Oldroyd-B-type model with fractional dissipation","authors":"Yichen Dai, Zhong Tan, Jiahong Wu","doi":"10.4310/cms.2023.v21.n5.a8","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n5.a8","url":null,"abstract":"","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"448 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70422263","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}
Pub Date : 2023-01-01DOI: 10.4310/cms.2023.v21.n6.a10
Ferdinando Auricchio, Giuseppe Toscani, Mattia Zanella
In this paper we study a novel Fokker-Planck-type model that is designed to mimic manufacturing processes through the dynamics characterizing a large set of agents. In particular, we describe a many-agent system interacting with a target domain in such a way that each agent/particle is attracted by the center of mass of the target domain with the aim to uniformly cover this zone. To this end, we first introduce a mean-field model with discontinuous flux whose large time behavior is such that the steady state is globally continuous and uniform over a connected portion of the domain. We prove that a diffusion coefficient that guarantees that a given portion of mass enters in the target domain exists and that it is unique. Furthermore, convergence to equilibrium in 1D is provided through a reformulation of the initial problem involving a nonconstant diffusion function. The extension to 2D is explored numerically by means of recently introduced structure preserving methods for Fokker-Planck equations.
{"title":"Fokker–Planck modeling of many-agent systems in swarm manufacturing: asymptotic analysis and numerical results","authors":"Ferdinando Auricchio, Giuseppe Toscani, Mattia Zanella","doi":"10.4310/cms.2023.v21.n6.a10","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n6.a10","url":null,"abstract":"In this paper we study a novel Fokker-Planck-type model that is designed to mimic manufacturing processes through the dynamics characterizing a large set of agents. In particular, we describe a many-agent system interacting with a target domain in such a way that each agent/particle is attracted by the center of mass of the target domain with the aim to uniformly cover this zone. To this end, we first introduce a mean-field model with discontinuous flux whose large time behavior is such that the steady state is globally continuous and uniform over a connected portion of the domain. We prove that a diffusion coefficient that guarantees that a given portion of mass enters in the target domain exists and that it is unique. Furthermore, convergence to equilibrium in 1D is provided through a reformulation of the initial problem involving a nonconstant diffusion function. The extension to 2D is explored numerically by means of recently introduced structure preserving methods for Fokker-Planck equations.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","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":"135783311","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}
Pub Date : 2023-01-01DOI: 10.4310/cms.2023.v21.n8.a8
Xiaoping Zhai, Yongsheng Li, Fujun Zhou
We study the global strong solutions to the compressible Navier-Stokes system with potential temperature transport in $mathbb{R}^n.$ Different from the Navier-Stokes-Fourier system, the pressure is a nonlinear function of the density and the potential temperature, we can not exploit the special quasi-diagonalization structure of this system to capture any dissipation of the density. Some new idea and delicate analysis involved in high or low frequency decomposition in the Besov spaces have to be made to close the energy estimates.
{"title":"Global strong solutions to the compressible Navier–Stokes system with potential temperature transport","authors":"Xiaoping Zhai, Yongsheng Li, Fujun Zhou","doi":"10.4310/cms.2023.v21.n8.a8","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n8.a8","url":null,"abstract":"We study the global strong solutions to the compressible Navier-Stokes system with potential temperature transport in $mathbb{R}^n.$ Different from the Navier-Stokes-Fourier system, the pressure is a nonlinear function of the density and the potential temperature, we can not exploit the special quasi-diagonalization structure of this system to capture any dissipation of the density. Some new idea and delicate analysis involved in high or low frequency decomposition in the Besov spaces have to be made to close the energy estimates.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"6 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":"135712017","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}
Pub Date : 2023-01-01DOI: 10.4310/cms.2023.v21.n6.a12
Hong Sun, Yanping Chen, Xuan Zhao
{"title":"Error estimate of the nonuniform $L1$ type formula for the time fractional diffusion-wave equation","authors":"Hong Sun, Yanping Chen, Xuan Zhao","doi":"10.4310/cms.2023.v21.n6.a12","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n6.a12","url":null,"abstract":"","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"117 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":"135649579","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}
Pub Date : 2023-01-01DOI: 10.4310/cms.2023.v21.n6.a8
Jinjing Liu, Meichen Hou
{"title":"Stability of contact discontinuity for an isentropic viscosity system with Chaplygin gas","authors":"Jinjing Liu, Meichen Hou","doi":"10.4310/cms.2023.v21.n6.a8","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n6.a8","url":null,"abstract":"","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"275 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":"135649916","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}
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