  We present a full classification of the short-time behaviour of the
interfaces and local solutions to the nonlinear parabolic $p$-Laplacian type
reaction-diffusion equation of non-Newtonian elastic filtration \[
u_t-\Big(|u_x|^{p-2}u_x\Big)_x+bu^{\beta}=0, \ p>2, \beta >0 \] The interface
may expand, shrink, or remain stationary as a result of the competition of the
diffusion and reaction terms near the interface, expressed in terms of the
parameters $p,\beta, sign~b$, and asymptotics of the initial function near its
support. In all cases, we prove the explicit formula for the interface and the
local solution with accuracy up to constant coefficients. The methods of the
proof are based on nonlinear scaling laws, and a barrier technique using
special comparison theorems in irregular domains with characteristic boundary
curves.
