Abstract
In the Kompaneets approximation, we study the propagation of a shock front from the explosion point in an inhomogeneous medium with a power-law variation of the density characterized by the exponent n=2, which is important and corresponds to the external parts of the solar and stellar coronas. An unexpectedly simple exact solution, which allows us to clarify the structure of the general solution under an arbitrary monotonous law of the density variation, was obtained. The results for the plane case are compared with Korikanskii’s results for a noncentral point explosion in a radially stratified medium. A correspondence between the exact solutions is established in these cases, and a new solution for the noncentral explosion is obtained for the case of a density with a singularity at a finite radius, which decreases quadratically at infinity.
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Additional information
Radioastronimical Institute of the National Academy of Sciences, Khar’kov, Ukraine; Research Institute of Physics, State University, Rostov-on-Don, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 41, No. 6, pp. 683–698, June, 1998.
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Kontorovich, V.M., Pimenov, S.F. An exact solution of the kompaneets equations for a strong point explosion in a medium with quadratic density decrease. Radiophys Quantum Electron 41, 457–468 (1998). https://doi.org/10.1007/BF02676679
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DOI: https://doi.org/10.1007/BF02676679