{"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":null,"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":3.6000,"publicationDate":"2023-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Models & Methods in Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/s021820252340002x","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 3
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.
期刊介绍：
The purpose of this journal is to provide a medium of exchange for scientists engaged in applied sciences (physics, mathematical physics, natural, and technological sciences) where there exists a non-trivial interplay between mathematics, mathematical modelling of real systems and mathematical and computer methods oriented towards the qualitative and quantitative analysis of real physical systems.
The principal areas of interest of this journal are the following:
1.Mathematical modelling of systems in applied sciences;
2.Mathematical methods for the qualitative and quantitative analysis of models of mathematical physics and technological sciences;
3.Numerical and computer treatment of mathematical models or real systems.
Special attention will be paid to the analysis of nonlinearities and stochastic aspects.
Within the above limitation, scientists in all fields which employ mathematics are encouraged to submit research and review papers to the journal. Both theoretical and applied papers will be considered for publication. High quality, novelty of the content and potential for the applications to modern problems in applied sciences and technology will be the guidelines for the selection of papers to be published in the journal. This journal publishes only articles with original and innovative contents.
Book reviews, announcements and tutorial articles will be featured occasionally.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
