Volume 4, Issue 3
Travelling Wave Front Solutions for Reaction-diffusion Systems

Li Zhengyuan, Ye Qixiao

J. Part. Diff. Eq.,4(1991),pp.1-14

Published online: 1991-04

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  • Abstract

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(-∞) = v(+∞) = 0 u(+∞) = v(-∞) = 1 where 0 < r < 1, 0 < b < \frac{1 - r}{r} are known constants and c is unknown constant to be obtained.

  • Keywords

Reaction-diffusion system travelling wave front solutions upperlower solution method B-Z reaction

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COPYRIGHT: © Global Science Press

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@Article{JPDE-4-1, author = {Li Zhengyuan, Ye Qixiao}, title = {Travelling Wave Front Solutions for Reaction-diffusion Systems}, journal = {Journal of Partial Differential Equations}, year = {1991}, volume = {4}, number = {3}, pages = {1--14}, abstract = { 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(-∞) = v(+∞) = 0 u(+∞) = v(-∞) = 1 where 0 < r < 1, 0 < b < \frac{1 - r}{r} are known constants and c is unknown constant to be obtained.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5771.html} }
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(-∞) = v(+∞) = 0 u(+∞) = v(-∞) = 1 where 0 < r < 1, 0 < b < \frac{1 - r}{r} are known constants and c is unknown constant to be obtained.
Li Zhengyuan, Ye Qixiao. (1970). Travelling Wave Front Solutions for Reaction-diffusion Systems. Journal of Partial Differential Equations. 4 (3). 1-14. doi:
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