Traveling waves for a Belousov–Zhabotinsky reaction–diffusion system with nonlocal effect. (April 2022) - Han, Bang-Sheng; Chang, Meng-Xue; Bo, Wei-Jian
Abstract: This paper is to consider the traveling wave solutions of a Belousov–Zhabotinsky reaction–diffusion system with nonlocal nonlinearity. By combining the super- and sub-solutions and Schauder's fixed point theorem, we first establish the existence and non-existence of traveling wave solutions connecting ( 0, 0 ) to an unknown positive steady state, which is independent of the intensity of nonlocality. Our results indicate that there is a critical speed c ∗ > 0 such that the traveling wave solution exists if c > c ∗, while the traveling wave solution does not exist if c < c ∗ . It is worth noting that the nonlocal effect has a great influence on the final state of traveling wave solutions at + ∞ .