Bautin, S. P. Existence of solutions to A. N. Krajko’s problem. (English. Russian original) Zbl 0958.76077 Prikl. Mekh. Tekh. Fiz. 41, No. 3, 48-55 (2000); translation in J. Appl. Mech. Tech. Phys. 41, No. 3, 421-428 (2000). The author considers initial-boundary value problems for plane, cylindrical, and spherical layers of ideal gas. An iterative solution of these problems provides a solution to Krajko’s problem on the isentropic transition of ideal gas from a homogeneous state of rest to another state of rest with higher or lower density. The author also proves the existence of locally analytic solutions. Reviewer: V.I.Pinchukov (Novosibirsk) Cited in 1 Document MSC: 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics Keywords:polytropic gas; reflection of rarefaction wave; uniqueness; plane layer; decay of weak discontinuity; cylindrical layer; spherical layer; initial-boundary value problems; Krajko’s problem; isentropic transition of ideal gas; existence; locally analytic solutions PDFBibTeX XMLCite \textit{S. P. Bautin}, Prikl. Mekh. Tekh. Fiz. 41, No. 3, 48--55 (2000; Zbl 0958.76077); translation in J. Appl. Mech. Tech. Phys. 41, No. 3, 421--428 (2000)