{"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":null,"pages":null},"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.
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