The stability of traveling wave fronts for Belousov-Zhabotinskii system with small delay

Wang, Lina; Zhao, Yingshun; Wu, Yanxia

doi:10.3934/dcdsb.2022246

Cited by 2 publications

(1 citation statement)

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“…where τ 0, and they used a monotonic iterative method to study the existence of the solution. For more research on the time delay case, refer to [14,[16][17][18][19][20]. Moreover, Du and Qiao [21] investigated the nonlocal effect (spatio-temporal delay) of v(x, t) as follows they obtained the existence of the traveling wave solution by singular perturbation method and established the asymptotic behavior of the solution using asymptotic theory.…”

Section: Introductionmentioning

confidence: 99%

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

Chang,

Han,

Yang

2024

Phys. Scr.

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We consider a Belousov-Zhabotinskii reaction-diﬀusion system with nonlocal eﬀects and study the existence of traveling wave solutions. By constructing appropriate super- and sub-solutions and using Schauder’s ﬁxed point theorem, we show that there is a critical speed c > 0 such that when the wave speed c > c , there exists a traveling wave solution connecting (0, 0) to an unknown positive steady-state, while there is no travelling wave solution when c < c . Moreover, we also examine a special case where ϕ1(x) is Dirac function, and demonstrate the existence of the traveling wave solution connecting the equilibria (0, 0) and (1, 1) for c > c , whereas the traveling wave solution does not exist when c < c . Finally, the long-time behavior of the solution is investigated through numerical simulation and theoretical analysis, and it is found that the choice of kernel functions and the setting of initial value conditions play a crucial role.

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