A variational problem for the spatial segregation of reaction-diffusion systems

被引：89
作者：
Conti, M
Terracini, S
Verzini, G
机构：
[1] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy
[2] Univ Milan, Dipartimento Matemat & Applicaz, I-20126 Milan, Italy
来源：
INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2005年 / 54卷 / 03期
关键词：
segregation states; multiple intersection points; monotonicity formula; regularity theory;
D O I：
10.1512/iumj.2005.54.2506
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we study a class of stationary states for reaction-diffusion systems of k >= 3 densities having disjoint supports. For a class of segregation states governed by a variational principle we prove existence and provide conditions for uniqueness. Some qualitative properties and the local regularity both of the densities and of their free boundaries are established in the more general context of a functional class characterized by differential inequalities.
引用
收藏
页码：779 / 815
页数：37
相关论文
共 30 条
[1]  
ALESSANDRINI G, 1987, ANN SCUOLA NORM SUP, V14, P229
[2]   VARIATIONAL-PROBLEMS WITH 2 PHASES AND THEIR FREE BOUNDARIES [J].
ALT, HW ;
CAFFARELLI, LA ;
FRIEDMAN, A .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1984, 282 (02) :431-461
[3]  
Athanasopoulos I, 2001, J REINE ANGEW MATH, V534, P1
[4]   BIFURCATION OF STEADY-STATE SOLUTIONS IN PREDATOR-PREY AND COMPETITION SYSTEMS [J].
BLAT, J ;
BROWN, KJ .
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1984, 97 :21-34
[5]   Some new monotonicity theorems with applications to free boundary problems [J].
Caffarelli, LA ;
Jerison, D ;
Kenig, CE .
ANNALS OF MATHEMATICS, 2002, 155 (02) :369-404
[6]   Regularity of a free boundary with application to the Pompeiu problem [J].
Caffarelli, LA ;
Karp, L ;
Shahgholian, H .
ANNALS OF MATHEMATICS, 2000, 151 (01) :269-292
[7]  
CAFFARELLI LA, UNPUB REGULARITY INH
[8]   An optimal partition problem related to nonlinear eigenvalues [J].
Conti, M ;
Terracini, S ;
Verzini, G .
JOURNAL OF FUNCTIONAL ANALYSIS, 2003, 198 (01) :160-196
[9]   Nehari's problem and competing species systems [J].
Conti, M ;
Terracini, S ;
Verzini, G .
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2002, 19 (06) :871-888
[10]   STABLE COEXISTENCE STATES IN THE VOLTERRA-LOTKA COMPETITION MODEL WITH DIFFUSION [J].
COSNER, C ;
LAZER, AC .
SIAM JOURNAL ON APPLIED MATHEMATICS, 1984, 44 (06) :1112-1132
123