  We prove the existence of the minimal speed of propagation $c_*(r,b,K) \in
[2\sqrt{1-r},2]$ for wavefronts in the Belousov-Zhabotinsky system with a
spatiotemporal interaction defined by the convolution with (possibly,
"fat-tailed") kernel $K$. The model is assumed to be monostable non-degenerate,
i.e. $r\in (0,1)$. The slowest wavefront is termed pushed or non-linearly
determined if its velocity $c_*(r,b,K) > 2\sqrt{1-r}$. We show that
$c_*(r,b,K)$ is close to 2 if i) positive system's parameter $b$ is
sufficiently large or ii) if $K$ is spatially asymmetric to one side (e.g. to
the left: in such a case, the influence of the right side concentration of the
bromide ion on the dynamics is more significant than the influence of the left
side). Consequently, this reveals two reasons for the appearance of pushed
wavefronts in the Belousov-Zhabotinsky reaction.
