On the shape of stationary solutions to a chemotaxis model with saturation

被引：1

作者：

Morimoto, Kotaro ^{[1
]}

机构：

[1] Kamakura Womens Univ, Elementary Sch, Kamakura, Kanagawa 2478511, Japan

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2014年 / 99卷

基金：

日本学术振兴会;

关键词：

Chemotaxis model; Saturation; Transition layer; Spike pattern; GIERER-MEINHARDT SYSTEM; LEAST-ENERGY SOLUTIONS; ASYMPTOTIC-BEHAVIOR; INTERNAL LAYERS; AGGREGATION; EXISTENCE; EQUATIONS; PATTERNS;

D O I：

10.1016/j.na.2013.12.020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are concerned with stationary solutions to the chemotaxis model with effect of saturation. We study the relation of effect of saturation to the asymptotic behavior of stationary solutions. There are several saturation effects, so-called, a weak saturation, a semi-strong saturation and a strong saturation. In the weak saturation case, it is known that there exist spike solutions. However, it is unclear what types of solutions appear in the semi-strong saturation case and the strong saturation case. In this paper, in case the domain is a ball we construct a rotationally symmetric bubble-shaped solution with a finite limiting radius for the interface under the semi-strong and the strong saturation effect. (C) 2014 Elsevier Ltd. All rights reserved.

引用

页码：95 / 115

页数：21

共 22 条

[1] EXISTENCE AND NONEXISTENCE OF POSITIVE RADIAL SOLUTIONS OF NEUMANN PROBLEMS WITH CRITICAL SOBOLEV EXPONENTS
ADIMURTHI
YADAVA, SL
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1991, 115 (03) : 275 - 296
[2] [Anonymous], 2005, PROGR NONLINEAR DIFF
[3] ASYMPTOTIC-BEHAVIOR OF SOLUTIONS OF ELLIPTIC-EQUATIONS WITH CRITICAL EXPONENTS AND NEUMANN BOUNDARY-CONDITIONS
BUDD, C
KNAAP, MC
PELETIER, LA
[J]. PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1991, 117 : 225 - 250
[4] delPino MA, 1995, T AM MATH SOC, V347, P4807
[5] Horstmann D., 2003, Jahresberichte DMV, V105, P103
[6] INITIATION OF SLIME MOLD AGGREGATION VIEWED AS AN INSTABILITY
KELLER, EF
SEGEL, LA
[J]. JOURNAL OF THEORETICAL BIOLOGY, 1970, 26 (03) : 399 - &
[7] Construction and asymptotic behavior of multi-peak solutions to the gierer-meinhardt system with saturation
Kurata, Kazuhiro
Morimoto, Kotaro
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2008, 7 (06) : 1443 - 1482
[8] EXISTENCE OF MULTIPLE SPIKE STATIONARY PATTERNS IN A CHEMOTAXIS MODEL WITH WEAK SATURATION
Kurata, Kazuhiro
Morimoto, Kotaro
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2011, 31 (01) : 139 - 164
[9] UNIQUENESS OF RADIAL SOLUTIONS OF SEMILINEAR ELLIPTIC-EQUATIONS
KWONG, MK
LI, Y
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 333 (01) : 339 - 363
[10] A system of reaction diffusion equations arising in the theory of reinforced random walks
Levine, HA
Sleeman, BD
[J]. SIAM JOURNAL ON APPLIED MATHEMATICS, 1997, 57 (03) : 683 - 730

← 1 2 3 →