摘要：This work proposes an asymptotic method of solution for a system of nonlinear
nonhomogeneous equations of one class of initial-boundary problems with an unknown
external boundary in the domain. The system of equations describes an adiabatic
spherical and symmetrical motion of a gravitating gas , while a moving detonating wave
(a spherical surface where the solution undergoes the first kind of discontinuity) is the
external boundary of the domain.
As the first test problem in this work considered nonavtomodel problem of a central
explosion followed by a thermonuclear detonation of a nonhomogeneous bounded with
vacuum, gas sphere that is balanced in its own gravitating field. The asymptotic method
of a thin shock layer is used for the motion law and the thermodynamic characteristics
of the medium are calculated. For the zero approximation of the detonating wave motion
layer of Couch's problem in particular case are solved exactly and in general case –
with numerical methods. Interpolation formulas and asymptotics are founded.
As the second test problem in this work considered nonavtomodel problem of a central
explosion followed by a thermonuclear detonation of a nonhomogeneous bounded with
interstellar space (vacuum), gas sphere (nonhomogeneous star) that is balanced in its
own gravitating field. The initial-boundary problem for a system of nonlinear
nonhomogeneous equations are solved with asymptotic method of a thin shock layer.
The first two approximations for the motion law and the thermodynamic characteristics
of the medium are calculated. For the zero approximation of the detonating wave motion
layer of Couch's problem are solved with numerical methods. Numerical results are
founded.
