{"title":"在抛物线-椭圆形凯勒-西格尔系统中通过轻微超线性退化抑制炸裂,该系统的运动依赖于信号","authors":"Aijing Lu, Jie Jiang","doi":"10.1016/j.nonrwa.2024.104190","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we consider an initial–Neumann boundary value problem for a parabolic–elliptic Keller–Segel system with signal-dependent motility and a source term. Previous research has rigorously shown that the source-free version of this system exhibits an infinite-time blowup phenomenon when dimension <span><math><mrow><mi>N</mi><mo>≥</mo><mn>2</mn></mrow></math></span>. In the current work, when <span><math><mrow><mi>N</mi><mo>≤</mo><mn>3</mn></mrow></math></span>, we establish uniform boundedness of global classical solutions with an additional source term that involves slightly super-linear degradation effect on the density, of a maximum growth order <span><math><mrow><mi>s</mi><mo>log</mo><mi>s</mi></mrow></math></span>, unveiling a sufficient blowup suppression mechanism. The motility function considered in our work takes a rather general form compared with recent works (Fujie and Jiang, 2020; Lyu and Wang, 2023) which were restricted to the monotone non-increasing case. The cornerstone of our proof lies in deriving an upper bound for the second component of the system and an entropy-like estimate, which are achieved through tricky comparison skills and energy methods, respectively.</p></div>","PeriodicalId":49745,"journal":{"name":"Nonlinear Analysis-Real World Applications","volume":"81 ","pages":"Article 104190"},"PeriodicalIF":1.8000,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Suppression of blowup by slightly superlinear degradation in a parabolic–elliptic Keller–Segel system with signal-dependent motility\",\"authors\":\"Aijing Lu, Jie Jiang\",\"doi\":\"10.1016/j.nonrwa.2024.104190\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, we consider an initial–Neumann boundary value problem for a parabolic–elliptic Keller–Segel system with signal-dependent motility and a source term. Previous research has rigorously shown that the source-free version of this system exhibits an infinite-time blowup phenomenon when dimension <span><math><mrow><mi>N</mi><mo>≥</mo><mn>2</mn></mrow></math></span>. In the current work, when <span><math><mrow><mi>N</mi><mo>≤</mo><mn>3</mn></mrow></math></span>, we establish uniform boundedness of global classical solutions with an additional source term that involves slightly super-linear degradation effect on the density, of a maximum growth order <span><math><mrow><mi>s</mi><mo>log</mo><mi>s</mi></mrow></math></span>, unveiling a sufficient blowup suppression mechanism. The motility function considered in our work takes a rather general form compared with recent works (Fujie and Jiang, 2020; Lyu and Wang, 2023) which were restricted to the monotone non-increasing case. The cornerstone of our proof lies in deriving an upper bound for the second component of the system and an entropy-like estimate, which are achieved through tricky comparison skills and energy methods, respectively.</p></div>\",\"PeriodicalId\":49745,\"journal\":{\"name\":\"Nonlinear Analysis-Real World Applications\",\"volume\":\"81 \",\"pages\":\"Article 104190\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2024-08-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Nonlinear Analysis-Real World Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1468121824001299\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Analysis-Real World Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1468121824001299","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Suppression of blowup by slightly superlinear degradation in a parabolic–elliptic Keller–Segel system with signal-dependent motility
In this paper, we consider an initial–Neumann boundary value problem for a parabolic–elliptic Keller–Segel system with signal-dependent motility and a source term. Previous research has rigorously shown that the source-free version of this system exhibits an infinite-time blowup phenomenon when dimension . In the current work, when , we establish uniform boundedness of global classical solutions with an additional source term that involves slightly super-linear degradation effect on the density, of a maximum growth order , unveiling a sufficient blowup suppression mechanism. The motility function considered in our work takes a rather general form compared with recent works (Fujie and Jiang, 2020; Lyu and Wang, 2023) which were restricted to the monotone non-increasing case. The cornerstone of our proof lies in deriving an upper bound for the second component of the system and an entropy-like estimate, which are achieved through tricky comparison skills and energy methods, respectively.
期刊介绍:
Nonlinear Analysis: Real World Applications welcomes all research articles of the highest quality with special emphasis on applying techniques of nonlinear analysis to model and to treat nonlinear phenomena with which nature confronts us. Coverage of applications includes any branch of science and technology such as solid and fluid mechanics, material science, mathematical biology and chemistry, control theory, and inverse problems.
The aim of Nonlinear Analysis: Real World Applications is to publish articles which are predominantly devoted to employing methods and techniques from analysis, including partial differential equations, functional analysis, dynamical systems and evolution equations, calculus of variations, and bifurcations theory.