Large mass boundary condensation patterns in the stationary Keller-Segel system

被引：22

作者：

del Pino, Manuel ^{[1
]}

Pistoia, Angela ^{[2
]}

Vaira, Giusi ^{[2
]}

机构：

[1] Univ Chile, Fac Ciencias Fis & Matemat, Dept Ingn Matemat, Casilla 170,Correo 3, Santiago, Chile

[2] Univ Roma La Sapienza, Dipartimento SBAI, Via Antonio Scarpa 16, I-00161 Rome, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2016年 / 261卷 / 06期

关键词：

Keller-Segel system; Boundary concentration; PERTURBED NEUMANN PROBLEM; STEADY-STATES; CHEMOTAXIS; CURVES;

D O I：

10.1016/j.jde.2016.05.032

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the boundary value problem { -Delta u + u = lambda e(u), in Omega partial derivative(v)u = 0 on partial derivative Omega where Omega is a bounded smooth domain in R-2, lambda > 0 and v is the inner normal derivative at partial derivative Omega. This problem is equivalent to the stationary Keller-Segel system from chemotaxis. We establish the existence of a solution u(lambda) which exhibits a sharp boundary layer along the entire boundary partial derivative Omega as lambda -> 0. These solutions have large mass in the sense that integral(Omega) lambda e(u lambda) similar to | log lambda|. (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：3414 / 3462

页数：49

共 18 条

[1]

[Anonymous], 2000, Adv. Math. Sci. Appl.

[2]

Biler P., 1998, Adv. Math. Sci. Appl., V8, P715

[3] UNIFORM ESTIMATES AND BLOW UP BEHAVIOR FOR SOLUTIONS OF -DELTA-U = V(X)EU IN 2 DIMENSIONS [J].