We have considered a stationary outflowing
envelope accelerated by the radiative force in
arbitrary optical depth case. Introduced
approximations provide satisfactory description of
the behavior of the matter flux with partially
separated radiation at arbitrary optical depths.
The obtained systemof differential equations
provides a continuous transition of the solution
between optically thin and optically thick
regions. We analytically derivedapproximate
representation of the solution at the vicinity of
the sonic point. Using this representation we
numerically integrate the system of equations from
the critical point to the infinity. Matching the
boundary conditions we obtain solutions describing
the problem system of differential equations. The
theoretical approach advanced in this work could
be useful for self-consistent simulations of
massive star evolution with mass loss.
In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.
Outflowing Envelopes From Stars at
Arbitrary Optical Depths a New Approach to the
Problem