Solution of kompaneets equation for shock front in the inhomogeneous medium with density changing in a form of the hyperbolic tangent (intermediate region and real time evolution)

Abstract

The analytical solution of Kompaneets equation, describing the evolution of the shock front in a planestratified medium for density distribution in a form of the hyperbolic tangent modeling the boundary molecular cloud – interstellar medium was obtained (intermediate region of the shock front). Obtained solution allows to build the complete solution, restore the whole shock front and investigate its evolution in real time for arbitrary values of parameters: density changes, scale of inhomogeneity and position of the explosion point.