TY - JOUR
T1 - Travelling Wave Front Solutions for Reaction-diffusion Systems
AU - Li Zhengyuan, Ye Qixiao
JO - Journal of Partial Differential Equations
VL - 3
SP - 1
EP - 14
PY - 1991
DA - 1991/04
SN - 4
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5771.html
KW - Reaction-diffusion system
KW -  travelling wave front solutions
KW -  upperlower solution method
KW -  B-Z reaction
AB -  In this paper by using upper-lower solution method, under appropriate assumptions on f and g the existence of travelling wave front solutions for the following reaction-diffusion system is proved: {u_t - u_{xx}, = f(u,v) v_t - v_{xx} = g(u, v) As an application, the necessary and sufficient condition of the existence of monotone solutions for the boundary value problem {u" + cu' + u(1 - u- rv) = 0 v" + cv' - buv = 0 u(-&#8734) = v(+&#8734) = 0 u(+&#8734) = v(-&#8734) = 1 where 0 < r < 1, 0 < b < \frac{1 - r}{r} are known constants and c is unknown constant to be obtained.