{"title":"A free boundary problem with resource-dependent motility in a weak heterogeneous environment","authors":"Dawei Zhang, Yun Huang, Chufen Wu, Jianshe Yu","doi":"10.1111/sapm.12684","DOIUrl":null,"url":null,"abstract":"<p>This paper is concerned with a free boundary problem with resource-dependent motility in a weak heterogeneous environment. The existence and uniqueness of global solutions are discussed first. Next, we establish long-time behaviors of solutions which is a spreading–vanishing dichotomy. Moreover, we obtain sharp criteria on spreading and vanishing by investigating the associated linearized eigenvalue problem. The theoretical analyses reveal an important biological phenomenon. (i) Resource abundance reduces the motility, providing advantages for individuals to persist in a habitat. (ii) Resource shortage enhances the motility, forcing individuals to expand outward to survive in an environment. Consequently, resource-dependent motility is more beneficial to the survival of species compared with random dispersal.</p>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"152 4","pages":"1456-1477"},"PeriodicalIF":2.6000,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studies in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/sapm.12684","RegionNum":2,"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: 0
Abstract
This paper is concerned with a free boundary problem with resource-dependent motility in a weak heterogeneous environment. The existence and uniqueness of global solutions are discussed first. Next, we establish long-time behaviors of solutions which is a spreading–vanishing dichotomy. Moreover, we obtain sharp criteria on spreading and vanishing by investigating the associated linearized eigenvalue problem. The theoretical analyses reveal an important biological phenomenon. (i) Resource abundance reduces the motility, providing advantages for individuals to persist in a habitat. (ii) Resource shortage enhances the motility, forcing individuals to expand outward to survive in an environment. Consequently, resource-dependent motility is more beneficial to the survival of species compared with random dispersal.
期刊介绍：
Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.
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