  A classical and a relativistic law of motion for a supernova remnant (SNR)
are deduced assuming an inverse power law behavior for the density of the
interstellar medium and applying the thin layer approximation. A third equation
of motion is found in the framework of relativistic hydrodynamics with
pressure, applying momentum conservation. These new formulas are calibrated
against a decade of observations of \snr. The existing knowledge of the
diffusive processes of ultrarelativistic electrons is reviewed in order to
explain the behavior of the `U' shaped profile of intensity versus distance
from the center of SN 1993J.
