Pyramidal traveling fronts in the Belousov-Zhabotinskii reaction-diffusion systems in R^3

Abstract

In this article, we consider a diffusion system with the Belousov-Zhabotinskii (BZ for short) chemical reaction. The existence and stability of V-shaped traveling fronts for the BZ system in \(\mathbb{R}^2\) had been proved in our previous papers [30, 31]. Here we establish the existence and stability of pyramidal traveling fronts for the BZ system in \(\mathbb{R}^3\).
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Traveling wave solution for a nonlocal Belousov-Zhabotinskii reaction-diffusion system

“…x Î e a , B ln . On the other hand, for any ξ ä [ − a, a], (U(ξ), V(ξ)) = (0, 0) can be a sub-solution to the problem (14), it consequently leads to U(ξ) > 0, V(ξ) > 0 for any ξ ä [ − a, a]. Thus, one has ( ) ( )…”

“…A lot of progress has been made, mainly focused on the existence, asymptotic behavior, stability and propagation speed of traveling wave solutions [4][5][6][7][8][9]. For the study of high-dimensional cases, refer to [10][11][12][13][14].…”

“…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.…”