Traveling waves for a Belousov–Zhabotinsky reaction–diffusion system with nonlocal effect

Traveling wave solution for a nonlocal Belousov-Zhabotinskii reaction-diffusion system

“…are super-and subsolutions of system (6), and the proof procedure is standard and can refer to [23], section 2, here we omit the specific steps. Define…”

“…and provided insight into the effect of different kernel functions on the asymptotic behavior of solution by numerical simulations. Furthermore, Han et al [23] explored the existence and non-existence of the traveling wave solutions of (5). For more research on similar models with nonlocal effects, see [24][25][26][27][28][29][30].…”

“…Motivated by the idea of [21,23,24], based on the study [23], we further take the nonlocal effect of v(x, t) into consideration. Natural questions are, what about the existence of the traveling wave solution in the system (1), and if so, what is the asymptotic behavior of the traveling wave solution?…”

Pyramidal traveling waves for a Belousov-Zhabotinskii system with obstacles

“…The properties of Belousov-Zhabotinskii reactiondiffusion system have been extensively studied, mainly focusing on traveling waves in R and planar traveling waves in R N (N ≥ 2), including the existence, non-existence, asymptotic behavior, stability and minimal wave speed of traveling waves [30,32,[48][49][50]53], and for numerical studies, see [36,37,44]. Moreover, for the results of time delay and non-local effects, see [11,16,29,35,54,57]. On the other hand, for non-planar traveling waves, Brazhnik and Davydov [9] predicted the existence of V -shaped traveling waves in the Belousov-Zhabotinskii system, which were subsequently verified by Pérez-Muñuzuri et al [43] in experiments.…”