Steady states with unbounded mass of the Keller-Segel system

被引：15

作者：

Pistoia, Angela ^{[1
]}

Vaira, Giusi ^{[1
]}

机构：

[1] Univ Roma La Sapienza, Dipartimento Sci Base & Applicate Ingn, I-00185 Rome, Italy

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2015年 / 145卷 / 01期

关键词：

PARABOLIC-ELLIPTIC SYSTEM; MODELING CHEMOTAXIS; RADIAL SOLUTIONS; POINT DYNAMICS; SINGULAR LIMIT; AGGREGATION; DIFFUSION; NONLINEARITIES; EXISTENCE; BEHAVIOR;

D O I：

10.1017/S0308210513000619

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the boundary-value problem -Delta u+u = lambda e(u) in B-r0, partial derivative(nu)u = 0 on partial derivative B-r0, where B-r0 is the ball of radius ro in R-N, N >= 2, lambda > 0 and v is the outer normal derivative at partial derivative B-r0. This problem is equivalent to the stationary Keller Segel system from chemotaxis. We show the existence of a solution concentrating at the boundary of the ball as lambda goes to 0.

引用

页码：203 / 222

页数：20

共 50 条

[1] Collapsing steady states of the Keller-Segel system
del Pino, Manuel
Wei, Juncheng
[J]. NONLINEARITY, 2006, 19 (03) : 661 - 684
[2] Keller-Segel System: A Survey on Radial Steady States
Casteras, Jean-Baptiste
[J]. NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, PICNDEA 2022, 2024, 7 : 57 - 74
[3] Layered solutions with unbounded mass for the Keller-Segel equation
Bonheure, Denis
Casteras, Jean-Baptiste
Noris, Benedetta
[J]. JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2017, 19 (01) : 529 - 558
[4] Unbounded mass radial solutions for the Keller-Segel equation in the disk
Bonheure, Denis
Casteras, Jean-Baptiste
Roman, Carlos
[J]. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2021, 60 (05)
[5] Uniqueness and convergence on equilibria of the Keller-Segel system with subcritical mass
Wang, Jun
Wang, Zhian
Yang, Wen
[J]. COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 2019, 44 (07) : 545 - 572
[6] Stabilization in the logarithmic Keller-Segel system
Winkler, Michael
Yokota, Tomomi
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2018, 170 : 123 - 141
[7] Large mass boundary condensation patterns in the stationary Keller-Segel system
del Pino, Manuel
Pistoia, Angela
Vaira, Giusi
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2016, 261 (06) : 3414 - 3462
[8] Generalised supersolutions with mass control for the Keller-Segel system with logarithmic sensitivity
Zhigun, Anna
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2018, 467 (02) : 1270 - 1286
[9] CRITICAL MASS ON THE KELLER-SEGEL SYSTEM WITH SIGNAL-DEPENDENT MOTILITY
Jin, Hai-Yang
Wang, Zhi-An
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2020, 148 (11) : 4855 - 4873
[10] A Keller-Segel type system in higher dimensions
Ulusoy, Suleyman
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2017, 34 (04): : 961 - 971

← 1 2 3 4 5 →