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Exact Solution of the Kompaneets Equation for Strong Explosion in Medium with Inverse-Square Decreasing Density

V. M. Kontorovich·S. F. Pimenov
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Abstract

In the framework of the Kompaneets approximation the propagation of a shock front (SF) in inhomogeneous medium with the power-law density decrease at the exponent $n=2$ is investigated. For this important case corresponding to outer regions of the solar and stellar coronas an unexpectedly simple exact solution clearing a structure of the general solution for an arbitrary monotonic density of medium is found. Our results for plane-layered medium are compared to the Korycansky one for off-centre explosion in radially stratified medium. The relation between the solutions in these media are found and a new exact solution for a noncentral explosion in the case of density singularity on the finite radius is received.

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V. M. Kontorovich, S. F. Pimenov. 1998-02-11. Exact Solution of the Kompaneets Equation for Strong Explosion in Medium with Inverse-Square Decreasing Density. https://arxiv.org/abs/astro-ph/9802149

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