On the problem of boundary conditions for mixed type equations arising in the description of astrophysical transonic flows
V.S. Beskin† a, b
T.I. Khalilov a
a Moscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141701, Russian Federation
b Lebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp. 53, Moscow, 119991, Russian Federation
Using the example of an exactly solvable problem, it is shown that the number of boundary conditions which is necessary to determine the transonic hydrodynamic flow near the so-called `nonstandard' singular point does not depend on whether the separatrix characteristic passes or does not pass through this point. Thus, a quite popular statement is called into question, according to which the critical surface, on which the regularity condition determines the flow structure, generally coincides with the surface of separatrix characteristics, and not with the sonic surface.