Kazhdan, Ya. M. Propagating of a spherical detonation wave in the expanding universe with an account for gravitation. (Russian. English summary) Zbl 0593.76076 Astron. Zh. 63, No. 3, 434-445 (1986). Summary: The self-similar solution of the equations describing a gas flow behind a divergent detonation wave in the matter expanding according to the Hubble law is carried out. For a narrow range of the adiabatic exponent x: 1\(<x<x_ 1\) \((1,2<x_ 1<1,21)\), there is a continuous solution in the whole region from the center to the front of the detonation wave with a weak discontinuity along the characteristic surface. If \(x>4/3\), a shock is formed in the flow behind the detonation wave front. If \(x_ 1<x\leq 4/3\), there is no self-similar solution to satisfy the physical conditions of the problem. Cited in 1 Review MSC: 76L05 Shock waves and blast waves in fluid mechanics 76Y05 Quantum hydrodynamics and relativistic hydrodynamics 83F05 Relativistic cosmology 83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.) Keywords:self-similar solution; gas flow behind a divergent detonation wave; Hubble law; narrow range of the adiabatic exponent; continuous solution; detonation wave with a weak discontinuity; characteristic surface; detonation wave PDFBibTeX XMLCite \textit{Ya. M. Kazhdan}, Astron. Zh. 63, No. 3, 434--445 (1986; Zbl 0593.76076)