Source-type solutions for equations of nonstationary filtration

The Cauchy problem for a given equation which arises in the study of phenomena occurring at the beginning of a nuclear explosion as well as the density in filtration of a gas through a porous medium is considered. The existence and uniqueness of a solution to this problem is proven. Also with certain restrictions it is proven that the solution tends asymptotically to the similar solution given previously. The asymptotic behavior of the solution at (0,0) is studied using a similarity transformation. 9 references. (JFP)