  The introduction of a exponential or power law gradient in the interstellar
medium (ISM) allows to produce an asymmetric evolution of the supernova remnant
(SNR) when the framework of the thin layer approximation is adopted.
Unfortunately both the exponential and power law gradients for the ISM do not
have a well defined physical meaning. The physics conversely is well
represented by an isothermal self-gravitating disk of particles whose velocity
is everywhere Maxwellian. . We derived a law of motion in the framework of the
thin layer approximation with a control parameter of the swept mass. The
photon's losses ,that are often neglected in the thin layer approximation, are
modeled trough a velocity dependence. The developed framework is applied to SNR
1987A and the three observed rings are simulated.
