Pub Date : 2023-07-14DOI: 10.1142/s0218202523020013
Youshan Tao, M. Winkler
This preface describes motivational aspects related to a special issue focusing on “analysis of complex chemotaxis models”, and briefly discusses the contributions provided by the six papers contained therein.
{"title":"Analysis of complex chemotaxis models","authors":"Youshan Tao, M. Winkler","doi":"10.1142/s0218202523020013","DOIUrl":"https://doi.org/10.1142/s0218202523020013","url":null,"abstract":"This preface describes motivational aspects related to a special issue focusing on “analysis of complex chemotaxis models”, and briefly discusses the contributions provided by the six papers contained therein.","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":" ","pages":""},"PeriodicalIF":3.5,"publicationDate":"2023-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44680953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-06DOI: 10.1142/s0218202523400067
Wei Wang
We consider the chemotaxis-Navier–Stokes system with gradient-dependent flux limitation and nonlinear production: [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] in a bounded domain [Formula: see text], where the flux limitation function [Formula: see text] and the signal production function [Formula: see text] generalize the prototypes [Formula: see text] and [Formula: see text] with [Formula: see text], [Formula: see text] and [Formula: see text]. For the linear production case of [Formula: see text], the global boundedness of solutions has been verified in the related literature for [Formula: see text]. In this paper, we expand to prove that the corresponding initial-boundary value problem possesses a unique globally bounded solution if [Formula: see text] for [Formula: see text], or if [Formula: see text] for [Formula: see text], which shows that when [Formula: see text], that is, the self-enhancement ability of chemoattractant is weak, the solutions still remain globally bounded even though the flux limitation is relaxed to permit proper [Formula: see text]; however, if [Formula: see text], it is necessary to impose the stronger flux limitation than that in the case [Formula: see text] to inhibit the possible finite-time blow-up. This seems to be the first result on the global solvability in the chemotaxis-Navier–Stokes model with nonlinear production.
{"title":"Global boundedness in a 2D chemotaxis-Navier–Stokes system with flux limitation and nonlinear production","authors":"Wei Wang","doi":"10.1142/s0218202523400067","DOIUrl":"https://doi.org/10.1142/s0218202523400067","url":null,"abstract":"We consider the chemotaxis-Navier–Stokes system with gradient-dependent flux limitation and nonlinear production: [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] in a bounded domain [Formula: see text], where the flux limitation function [Formula: see text] and the signal production function [Formula: see text] generalize the prototypes [Formula: see text] and [Formula: see text] with [Formula: see text], [Formula: see text] and [Formula: see text]. For the linear production case of [Formula: see text], the global boundedness of solutions has been verified in the related literature for [Formula: see text]. In this paper, we expand to prove that the corresponding initial-boundary value problem possesses a unique globally bounded solution if [Formula: see text] for [Formula: see text], or if [Formula: see text] for [Formula: see text], which shows that when [Formula: see text], that is, the self-enhancement ability of chemoattractant is weak, the solutions still remain globally bounded even though the flux limitation is relaxed to permit proper [Formula: see text]; however, if [Formula: see text], it is necessary to impose the stronger flux limitation than that in the case [Formula: see text] to inhibit the possible finite-time blow-up. This seems to be the first result on the global solvability in the chemotaxis-Navier–Stokes model with nonlinear production.","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":" ","pages":""},"PeriodicalIF":3.5,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44511022","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-23DOI: 10.1142/s0218202523400079
X. Mao, Yuxiang Li
{"title":"Critical Mass for Keller-Segel Systems with Supercritical Nonlinear Sensitivity","authors":"X. Mao, Yuxiang Li","doi":"10.1142/s0218202523400079","DOIUrl":"https://doi.org/10.1142/s0218202523400079","url":null,"abstract":"","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":" ","pages":""},"PeriodicalIF":3.5,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44709012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-23DOI: 10.1142/s0218202523400031
Ji Liu
{"title":"Global Classical Solvability and Stabilization in a Two-Dimensional Chemotaxis-Fluid System with Sub-Logarithmic Sensitivity","authors":"Ji Liu","doi":"10.1142/s0218202523400031","DOIUrl":"https://doi.org/10.1142/s0218202523400031","url":null,"abstract":"","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":" ","pages":""},"PeriodicalIF":3.5,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41428670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-23DOI: 10.1142/s021820252340002x
Fanze Kong, Juncheng Wei, Liangshun Xu
The Keller–Segel model is a paradigm to describe the chemotactic mechanism, which plays a vital role on the physiological and pathological activities of uni-cellular and multi-cellular organisms. One of the most interesting variants is the coupled system with the intrinsic growth, which admits many complex non-trivial patterns. This paper is devoted to the construction of multi-spiky solutions to the Keller–Segel models with the logistic source in 2D. Assuming that the chemo-attractive rate is large, we employ the inner-outer gluing scheme to nonlocal cross-diffusion system and prove the existence of multiple boundary and interior spikes. The numerical simulations are presented to highlight our theoretical results.
{"title":"Existence of Multi-spikes in the Keller-Segel model with Logistic Growth","authors":"Fanze Kong, Juncheng Wei, Liangshun Xu","doi":"10.1142/s021820252340002x","DOIUrl":"https://doi.org/10.1142/s021820252340002x","url":null,"abstract":"The Keller–Segel model is a paradigm to describe the chemotactic mechanism, which plays a vital role on the physiological and pathological activities of uni-cellular and multi-cellular organisms. One of the most interesting variants is the coupled system with the intrinsic growth, which admits many complex non-trivial patterns. This paper is devoted to the construction of multi-spiky solutions to the Keller–Segel models with the logistic source in 2D. Assuming that the chemo-attractive rate is large, we employ the inner-outer gluing scheme to nonlocal cross-diffusion system and prove the existence of multiple boundary and interior spikes. The numerical simulations are presented to highlight our theoretical results.","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":" ","pages":""},"PeriodicalIF":3.5,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43359181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-09DOI: 10.1142/s0218202523500483
D. Adak, Verónica Anaya, M. Bendahmane, D. Mora
{"title":"Conforming and nonconforming virtual element methods for fourth order nonlocal reaction diffusion equation","authors":"D. Adak, Verónica Anaya, M. Bendahmane, D. Mora","doi":"10.1142/s0218202523500483","DOIUrl":"https://doi.org/10.1142/s0218202523500483","url":null,"abstract":"","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":" ","pages":""},"PeriodicalIF":3.5,"publicationDate":"2023-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47134731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-06-09DOI: 10.1142/s0218202523500471
Renhai Wang, B. Guo, Daiwen Huang
{"title":"Necessary and Sufficient Criteria for Existence, Regularity and Asymptotic Stability of Enhanced Pullback Attractors with Applications to 3D Primitive Equations","authors":"Renhai Wang, B. Guo, Daiwen Huang","doi":"10.1142/s0218202523500471","DOIUrl":"https://doi.org/10.1142/s0218202523500471","url":null,"abstract":"","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":" ","pages":""},"PeriodicalIF":3.5,"publicationDate":"2023-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46618692","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-21DOI: 10.1142/s0218202523500446
Jiashan Zheng, Yuanyuan Ke
{"title":"Boundedness and large time behavior of solutions of a higher-dimensional haptotactic system modeling oncolytic virotherapy","authors":"Jiashan Zheng, Yuanyuan Ke","doi":"10.1142/s0218202523500446","DOIUrl":"https://doi.org/10.1142/s0218202523500446","url":null,"abstract":"","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":"1024 ","pages":""},"PeriodicalIF":3.5,"publicationDate":"2023-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41271661","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-13DOI: 10.1142/s0218202523500392
J. Campos, Carlos Pulido, J. Soler, Mario Veruete
{"title":"Singular patterns in Keller–Segel-type models","authors":"J. Campos, Carlos Pulido, J. Soler, Mario Veruete","doi":"10.1142/s0218202523500392","DOIUrl":"https://doi.org/10.1142/s0218202523500392","url":null,"abstract":"","PeriodicalId":49860,"journal":{"name":"Mathematical Models & Methods in Applied Sciences","volume":" ","pages":""},"PeriodicalIF":3.5,"publicationDate":"2023-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49225205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"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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