Self-similar blow-up for a reaction-diffusion system

被引：73
作者：
Herrero, MA
Medina, E
Velazquez, JJL
机构：
[1] Univ Complutense Madrid, Fac Matemat, Dept Matemat Aplicada, E-28040 Madrid, Spain
[2] Univ Cadiz, Fac Ciencias, Dept Matemat, Puerto Real 11510, Cadiz, Spain
来源：
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1998年 / 97卷 / 1-2期
关键词：
reaction-diffusion systems; blow-up; self-similar behaviour; matched asymptotic expansions;
D O I：
10.1016/S0377-0427(98)00104-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This work is concerned with the following system: [GRAPHICS] which is a model to describe several phenomena in which aggregation plays a crucial role as, for instance, motion of bacteria by chemotaxis and equilibrium of self-attracting clusters. When the space dimension N is equal to three, we show here that (S) has radial solutions with finite mass that blow-up in finite time in a self-similar manner. When N = 2, however, no radial solution with finite mass may give rise to self-similar blow-up. (C) 1989 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：99 / 119
页数：21
相关论文
共 17 条
[1]  
BILER P, IN PRESS ADV MATH SC
[2]   NON-LINEAR ASPECTS OF CHEMOTAXIS [J].
CHILDRESS, S ;
PERCUS, JK .
MATHEMATICAL BIOSCIENCES, 1981, 56 (3-4) :217-237
[3]   ANALYSIS OF THE EARLY STAGE OF THERMAL RUNAWAY [J].
DOLD, JW .
QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 1985, 38 (AUG) :361-387
[4]  
Galaktionov V. A., 1986, DIFF URAVN, V22, P1285
[5]   ASYMPTOTICALLY SELF-SIMILAR BLOW-UP OF SEMILINEAR HEAT-EQUATIONS [J].
GIGA, Y ;
KOHN, RV .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1985, 38 (03) :297-319
[6]   Singularity patterns in a chemotaxis model [J].
Herrero, MA ;
Velazquez, JJL .
MATHEMATISCHE ANNALEN, 1996, 306 (03) :583-623
[7]   Chemotactic collapse for the Keller-Segel model [J].
Herrero, MA ;
Velazquez, JJL .
JOURNAL OF MATHEMATICAL BIOLOGY, 1996, 35 (02) :177-194
[8]   Finite-time aggregation into a single point in a reaction-diffusion system [J].
Herrero, MA ;
Medina, E ;
Velazquez, JJL .
NONLINEARITY, 1997, 10 (06) :1739-1754
[9]  
HERRERO MA, IN PRESS ANN SCUOLA
[10]   ON EXPLOSIONS OF SOLUTIONS TO A SYSTEM OF PARTIAL-DIFFERENTIAL EQUATIONS MODELING CHEMOTAXIS [J].
JAGER, W ;
LUCKHAUS, S .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 329 (02) :819-824
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