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Uniqueness and convergence on equilibria of the Keller-Segel system with subcritical mass
Wang, Jun1; Wang, Zhian2; Yang, Wen3
2019-07-03
Source PublicationCOMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
ISSN0360-5302
Volume44Issue:7Pages:545-572
AbstractThis paper is concerned with the uniqueness of solutions to the following nonlocal semi-linear elliptic equationwhere omega is a bounded domain in and are positive parameters. The above equation arises as the stationary problem of the well-known classical Keller-Segel model describing chemotaxis. For Eq. (*) with Neumann boundary condition, we establish an integral inequality and prove that the solution of Eq. (*) is unique if and u satisfies some symmetric properties. While for Eq. (*) with Dirichlet boundary condition, the same uniqueness result is obtained without symmetric condition by a different approach inspired by some recent works (Gui and Moradifam, 2018, Invent. Math. 214(3):1169-1204; Gui and Moradifam, Proc. Am. Math. Soc. 146(3):1231-1124). As an application of the uniqueness results, we prove that the radially symmetric solution of the classical Keller-Segel system with subcritical mass subject to Neumann boundary conditions will converge to the unique constant equilibrium as time tends to infinity if omega is a disc in two dimensions. As far as we know, this is the first result that asserts the exact asymptotic behavior of solutions to the classical Keller-Segel system with subcritical mass in two dimensions.
KeywordKeller-Segel system mean field equation subcritical-mass uniqueness
Funding OrganizationHong Kong Polytechnic University ; Hong Kong Polytechnic University ; NSFC of China ; NSFC of China ; Fellowship of Outstanding Young Scholars of Jiangsu Province ; Fellowship of Outstanding Young Scholars of Jiangsu Province ; Six big talent peaks project in Jiangsu Province ; Six big talent peaks project in Jiangsu Province ; NSF of Jiangsu Province ; NSF of Jiangsu Province ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; NSFC ; NSFC ; project G-YBKT ; project G-YBKT ; Hong Kong Polytechnic University ; Hong Kong Polytechnic University ; NSFC of China ; NSFC of China ; Fellowship of Outstanding Young Scholars of Jiangsu Province ; Fellowship of Outstanding Young Scholars of Jiangsu Province ; Six big talent peaks project in Jiangsu Province ; Six big talent peaks project in Jiangsu Province ; NSF of Jiangsu Province ; NSF of Jiangsu Province ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; NSFC ; NSFC ; project G-YBKT ; project G-YBKT ; Hong Kong Polytechnic University ; Hong Kong Polytechnic University ; NSFC of China ; NSFC of China ; Fellowship of Outstanding Young Scholars of Jiangsu Province ; Fellowship of Outstanding Young Scholars of Jiangsu Province ; Six big talent peaks project in Jiangsu Province ; Six big talent peaks project in Jiangsu Province ; NSF of Jiangsu Province ; NSF of Jiangsu Province ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; NSFC ; NSFC ; project G-YBKT ; project G-YBKT ; Hong Kong Polytechnic University ; Hong Kong Polytechnic University ; NSFC of China ; NSFC of China ; Fellowship of Outstanding Young Scholars of Jiangsu Province ; Fellowship of Outstanding Young Scholars of Jiangsu Province ; Six big talent peaks project in Jiangsu Province ; Six big talent peaks project in Jiangsu Province ; NSF of Jiangsu Province ; NSF of Jiangsu Province ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; NSFC ; NSFC ; project G-YBKT ; project G-YBKT
DOI10.1080/03605302.2019.1581804
WOS KeywordMEAN-FIELD EQUATIONS ; STATISTICAL-MECHANICS ; CHEMOTAXIS MODEL ; BLOW-UP ; SYMMETRY ; INEQUALITY ; EXISTENCE
Language英语
Funding ProjectHong Kong Polytechnic University[PolyU 153041/15P] ; NSFC of China[11571140] ; NSFC of China[11671077] ; Fellowship of Outstanding Young Scholars of Jiangsu Province[BK20160063] ; Six big talent peaks project in Jiangsu Province[XYDXX-015] ; NSF of Jiangsu Province[BK20150478] ; CAS Pioneer Hundred Talents Program[Y8Y3011001] ; NSFC[11801550] ; project G-YBKT
Funding OrganizationHong Kong Polytechnic University ; Hong Kong Polytechnic University ; NSFC of China ; NSFC of China ; Fellowship of Outstanding Young Scholars of Jiangsu Province ; Fellowship of Outstanding Young Scholars of Jiangsu Province ; Six big talent peaks project in Jiangsu Province ; Six big talent peaks project in Jiangsu Province ; NSF of Jiangsu Province ; NSF of Jiangsu Province ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; NSFC ; NSFC ; project G-YBKT ; project G-YBKT ; Hong Kong Polytechnic University ; Hong Kong Polytechnic University ; NSFC of China ; NSFC of China ; Fellowship of Outstanding Young Scholars of Jiangsu Province ; Fellowship of Outstanding Young Scholars of Jiangsu Province ; Six big talent peaks project in Jiangsu Province ; Six big talent peaks project in Jiangsu Province ; NSF of Jiangsu Province ; NSF of Jiangsu Province ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; NSFC ; NSFC ; project G-YBKT ; project G-YBKT ; Hong Kong Polytechnic University ; Hong Kong Polytechnic University ; NSFC of China ; NSFC of China ; Fellowship of Outstanding Young Scholars of Jiangsu Province ; Fellowship of Outstanding Young Scholars of Jiangsu Province ; Six big talent peaks project in Jiangsu Province ; Six big talent peaks project in Jiangsu Province ; NSF of Jiangsu Province ; NSF of Jiangsu Province ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; NSFC ; NSFC ; project G-YBKT ; project G-YBKT ; Hong Kong Polytechnic University ; Hong Kong Polytechnic University ; NSFC of China ; NSFC of China ; Fellowship of Outstanding Young Scholars of Jiangsu Province ; Fellowship of Outstanding Young Scholars of Jiangsu Province ; Six big talent peaks project in Jiangsu Province ; Six big talent peaks project in Jiangsu Province ; NSF of Jiangsu Province ; NSF of Jiangsu Province ; CAS Pioneer Hundred Talents Program ; CAS Pioneer Hundred Talents Program ; NSFC ; NSFC ; project G-YBKT ; project G-YBKT
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000467816800001
PublisherTAYLOR & FRANCIS INC
Citation statistics
Document Type期刊论文
Identifierhttp://ir.wipm.ac.cn/handle/112942/13625
Collection中国科学院武汉物理与数学研究所
Corresponding AuthorYang, Wen
Affiliation1.Jiangsu Univ, Fac Sci, Zhenjiang, Jiangsu, Peoples R China
2.Hong Kong Polytech Univ, Dept Appl Math, Hung Hom, Kowloon, Hong Kong, Peoples R China
3.Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Hubei, Peoples R China
Recommended Citation
GB/T 7714
Wang, Jun,Wang, Zhian,Yang, Wen. Uniqueness and convergence on equilibria of the Keller-Segel system with subcritical mass[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,2019,44(7):545-572.
APA Wang, Jun,Wang, Zhian,&Yang, Wen.(2019).Uniqueness and convergence on equilibria of the Keller-Segel system with subcritical mass.COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS,44(7),545-572.
MLA Wang, Jun,et al."Uniqueness and convergence on equilibria of the Keller-Segel system with subcritical mass".COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS 44.7(2019):545-572.
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