Pub Date : 2023-09-22DOI: 10.4310/cms.2023.v21.n6.a14
Philippe Laurençot
Global weak solutions to a chemotaxis model with local sensing and consumption are shown to converge to spatially homogeneous steady states in the large time limit, when the motility is assumed to be positive and $C^1$-smooth on $[0,infty)$. The result is valid in arbitrary space dimension $n geq1$ and extends a previous result which only deals with space dimensions $n in {lbrace 1,2,3 rbrace}$.
具有局部感知和消耗的趋化性模型的全局弱解在大时间限制下收敛到空间均匀稳态，当运动假设为正且$[0,infty)$上$C^1$ -光滑时。该结果适用于任意空间维度$n geq1$，并扩展了先前仅处理空间维度$n in {lbrace 1,2,3 rbrace}$的结果。
{"title":"Long term spatial homogeneity for a chemotaxis model with local sensing and consumption","authors":"Philippe Laurençot","doi":"10.4310/cms.2023.v21.n6.a14","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n6.a14","url":null,"abstract":"Global weak solutions to a chemotaxis model with local sensing and consumption are shown to converge to spatially homogeneous steady states in the large time limit, when the motility is assumed to be positive and $C^1$-smooth on $[0,infty)$. The result is valid in arbitrary space dimension $n geq1$ and extends a previous result which only deals with space dimensions $n in {lbrace 1,2,3 rbrace}$.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"1226 ","pages":""},"PeriodicalIF":1.0,"publicationDate":"2023-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138515172","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.a5
Dandan Ding, Zhong Tan, Zhonger Wu
{"title":"The global generalized solution of the chemotaxis-Navier–Stokes system with logistic source","authors":"Dandan Ding, Zhong Tan, Zhonger Wu","doi":"10.4310/cms.2023.v21.n6.a5","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n6.a5","url":null,"abstract":"","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"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":"135649583","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.a7
Claudius Birke, Christophe Chalons, Christian Klingenberg
We present a numerical approximation of the solutions of the Euler equations with a gravitational source term. On the basis of a Suliciu type relaxation model with two relaxation speeds, we construct an approximate Riemann solver, which is used in a first order Godunov-type finite volume scheme. This scheme can preserve both stationary solutions and the low Mach limit to the corresponding incompressible equations. In addition, we prove that our scheme preserves the positivity of density and internal energy, that it is entropy satisfying and also guarantees not to give rise to numerical checkerboard modes in the incompressible limit. Later we give an extension to second order that preserves positivity, asymptotic-preserving and well-balancing properties. Finally, the theoretical properties are investigated in numerical experiments.
{"title":"A low Mach two-speed relaxation scheme for the compressible Euler equations with gravity","authors":"Claudius Birke, Christophe Chalons, Christian Klingenberg","doi":"10.4310/cms.2023.v21.n8.a7","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n8.a7","url":null,"abstract":"We present a numerical approximation of the solutions of the Euler equations with a gravitational source term. On the basis of a Suliciu type relaxation model with two relaxation speeds, we construct an approximate Riemann solver, which is used in a first order Godunov-type finite volume scheme. This scheme can preserve both stationary solutions and the low Mach limit to the corresponding incompressible equations. In addition, we prove that our scheme preserves the positivity of density and internal energy, that it is entropy satisfying and also guarantees not to give rise to numerical checkerboard modes in the incompressible limit. Later we give an extension to second order that preserves positivity, asymptotic-preserving and well-balancing properties. Finally, the theoretical properties are investigated in numerical experiments.","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"9 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":"135712012","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.n7.a1
Haiyang Wang, Zhen Wu
{"title":"A kind of time-inconsistent corporate international investment problem with discontinuous cash flow","authors":"Haiyang Wang, Zhen Wu","doi":"10.4310/cms.2023.v21.n7.a1","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n7.a1","url":null,"abstract":"","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"148 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":"136052542","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.n2.a4
Chunxiong Zheng, Jia Yin
{"title":"Generalized integral equation method for an elliptic nonlocal equation in measure space","authors":"Chunxiong Zheng, Jia Yin","doi":"10.4310/cms.2023.v21.n2.a4","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n2.a4","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":"70421549","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.n2.a6
Tingting Zhu
{"title":"Emergent behaviors of Kuramoto model with frustration under switching topology","authors":"Tingting Zhu","doi":"10.4310/cms.2023.v21.n2.a6","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n2.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":"70422291","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.a13
Qi Guo, Yamin Xiao
{"title":"The initial-boundary value problem for the Landau–Lifshitz equation with Gilbert damping term","authors":"Qi Guo, Yamin Xiao","doi":"10.4310/cms.2023.v21.n6.a13","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n6.a13","url":null,"abstract":"","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"293 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":"135649582","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.a7
Guoqiang Ren, Bin Liu
{"title":"Boundedness in a three-dimensional chemotaxis-Stokes system involving a subcritical sensitivity and indirect signal production","authors":"Guoqiang Ren, Bin Liu","doi":"10.4310/cms.2023.v21.n6.a7","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n6.a7","url":null,"abstract":"","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"26 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":"135649886","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.a3
Shibin Dai, Joseph Renzi, Steven M. Wise
{"title":"Gamma convergence for the de Gennes–Cahn–Hilliard energy","authors":"Shibin Dai, Joseph Renzi, Steven M. Wise","doi":"10.4310/cms.2023.v21.n8.a3","DOIUrl":"https://doi.org/10.4310/cms.2023.v21.n8.a3","url":null,"abstract":"","PeriodicalId":50659,"journal":{"name":"Communications in Mathematical Sciences","volume":"34 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":"135711813","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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