On some unbounded solutions of piston problem

The paper continues the research of blow-up boundary problem in compressible media. The compression of the ideal gas by means of plane piston, moving according to the blow-up law, is examined. The nonlocalized gasdynamic movement (i.e. gasdynamic function increase infinitely in infinite area in limited time) is investigated. The known particular solutions are considered. It is shown, that these flows are described by exponential and power self-similar solutions. The criteria of existences and uniqueness of solutions in dependence of the medium properties, the initial conditions and the boundary law is formulated.
The research has shown, that “fast” blow-up boundary modes ($\mathrm{HS}$-modes) leads to nonlocalized flows, unlike “slow” ones ($\mathrm{S}$-modes, the solution with separation of space and time variables).