New conditions for pattern solutions of a Brusselator model  

作　　者：TONG Chang-qing LIN Jia-yun MA Man-jun TAO Ji-cheng 

机构地区：[1]Department of mathematics,Hangzhou Dianzi University,Hangzhou 310018,China [2]Department of Mathematics,Zhejiang Sci-tech University,Hangzhou 310018,China [3]Department of mathematics,College of Science,China Jiliang University,Hangzhou 310018,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2019年第4期460-467,共8页高校应用数学学报（英文版）（B辑）

基　　金：supported by the National Natural Science Foundation of China(No.11671359);the Science Foundation of Zhejiang Sci-Tech University under Grant No.15062173-Y;supported by the provincial Natural Science Foundation of Zhejiang(LY16A010009)

摘　　要：This paper is devoted to establishing a critical value of the concentration of one intermediary reactant which determines whether pattern solutions of a class of Brusselator models exist or not.We introduce a new method to compute the degree index of the related linear operator so that the obtained sufficient conditions are easier to verify than those in the known references.The proofs mainly rely on Leray-Schauder degree theory,implicit function theorem and analytical techniques.This paper is devoted to establishing a critical value of the concentration of one intermediary reactant which determines whether pattern solutions of a class of Brusselator models exist or not. We introduce a new method to compute the degree index of the related linear operator so that the obtained sufficient conditions are easier to verify than those in the known references. The proofs mainly rely on Leray-Schauder degree theory, implicit function theorem and analytical techniques.

关 键 词：BRUSSELATOR model PATTERN solution DEGREE INDEX THEORY 

分 类 号：O17[理学—数学]