STABILITY IMPLIES CONSTANCY FOR FULLY AUTONOMOUS REACTION-DIFFUSION-EQUATIONS ON FINITE METRIC GRAPHS

被引：1
作者：
von Below, Joachim [1 ]
Lubary, Jose A. [2 ]
机构：
[1] Univ Lille Nord France, LMPA Joseph Liouville ULCO, FR CNRS Math 2956, 50 Rue F Buisson,CS 80699, F-62228 Calais, France
[2] Univ Politecn Cataluna, Dept Matemat, Campus Nord,Edifici Ordi Girona 1-3, ES-08034 Barcelona, Spain
来源：
NETWORKS AND HETEROGENEOUS MEDIA | 2018年 / 13卷 / 04期
关键词：
Reaction-diffusion-equations; metric graphs; quantum graphs; net-; works; attractors; stability; STATES;
D O I：
10.3934/nhm.2018031
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that there are no stable stationary nonconstant solutions of the evolution problem (1) for fully autonomous reaction-diffusion-equations on the edges of a finite metric graph G under continuity and Kirchhoff flow transition conditions at the vertices. (1) {u is an element of C(G X [0,infinity)) boolean AND C-K(2,1)(G X (0,infinity)), partial derivative(t)u(j )= partial derivative(2)(j)u(j) + f(u(j)) on the edges k(j), (K) Sigma(N)(j=1)d(ij)c(ij)partial derivative(j)u(j) (v(i), t) = 0 at the vertices v(i).( )
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页码：691 / 717
页数：27
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