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Аn analytical solution for a spherically stratified medium is constructed on the strength of an earlier obtained exact solution of Kompaneets equation for the shock front in a planar stratified medium with the density changing as the hyperbolic tangent. The solution obtained allows to build entirely the shock front and explore its evolution for different values of independent parameters (density gradient, explosion point position, scale of inhomogeneity) which varying can permit simulation of real conditions while obtaining information on medium properties and supernova remnant evolution.