Partially invariant solutions for a submodel of radial motions of a gas
Abstract
All partially invariant solutions in terms of the group of extensions for a model of radial motions of an ideal gas are found. The solutions are obtained by the method of separation of variables in an equation containing functions of one variable but different functions of different independent variables. The solutions predict different continuous unsteady convergence or expansion of the gas under the action of a piston with a point sink or source. If the sink or source affects all particles simultaneously, a collapse or an explosion occurs.
 Publication:

Journal of Applied Mechanics and Technical Physics
 Pub Date:
 September 2007
 DOI:
 10.1007/s108080070082z
 Bibcode:
 2007JAMTP..48..641K
 Keywords:

 radial motion of the gas;
 collapse;
 source;
 separation of variables