Pyramidal traveling fronts in the Belousov-Zhabotinskii reaction-diffusion systems in \(\mathbb{R}^3\). (English) Zbl 1454.35045
Summary: 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 [H.-T. Niu et al., J. Differ. Equations 264, No. 9, 5758–5801 (2018; Zbl 1394.35220); Nonlinear Anal., Real World Appl. 46, 493–524 (2019; Zbl 1409.35097)]. Here we establish the existence and stability of pyramidal traveling fronts for the BZ system in \(\mathbb{R}^3\).
MSC:
| 35C07 | Traveling wave solutions |
| 35K45 | Initial value problems for second-order parabolic systems |
| 35K57 | Reaction-diffusion equations |
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 92E20 | Classical flows, reactions, etc. in chemistry |
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