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).( )

引用

页码：691 / 717

页数：27

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