摘要
We study the effect of a complexation reaction on the propagation of reaction fronts in the quadratic auto catalytic reaction system. The quadratic auto catalytic reaction, a pivotal step in many reaction systems, is closely monitored by the complexing agent, which tracks the reaction process and locates the position of the reaction front, underscoring its significance. Thus, it is interesting to study how the complexation reaction affects traveling waves in the quadratic auto catalytic system. Two critical questions on traveling waves of a system are (1) does there exist a vmin such that a traveling wave with speed v exists if and only if v > vmin and (2) if such a vmin exists, is the minimum wave speed vmin derived from the linearization of the system at the unstable steady state? For the quadratic auto catalytic reaction system without complexation reactions, the answers to these two questions are affirmative. However, in the presence of a complexing agent, we give sufficient conditions for linear and nonlinear minimal speed selection mechanisms in different parameter regimes. Our findings reveal that the complex agent, far from being a passive observer, plays a dynamic and active role in the wave propagation of the quadratic auto catalytic reaction system, significantly impacting its behavior.