On the perturbation front structure for transport processes with spatial–temporal nonlocality

The one-dimensional problem of the propagation of a perturbation front from a point instantaneous source for transport processes with spatial–temporal nonlocality is considered. A class of nonlocality kernels with a singularity of the form $t^{-1}$ for small times is used. The front propagation speed $v$ is calculated and an expression for perturbations in the vicinity of the front is derived in the form of an asymptotic series in powers of the parameter $\tau=t-xv^{-1}$.