Reinicke, P.; Meyer-ter-Vehn, J. The point explosion with heat conduction. (English) Zbl 0745.76071 Phys. Fluids, A 3, No. 7, 1807-1818 (1991). The influence of nonlinear heat conduction is investigated for strong point explosions in an ambient gas. An ideal gas equation of state and a heat conductivity depending on temperature and density in ower-law form are assumed. It is shown that two sherical waves are obtained — a shock wave and a heat wave. They have sharp fronts which run at different speeds, in general, and in a relative order depending on parameters and time. Starting from the underlying Lie group symmetry, self-similar solutions of the problem are discussed in detail; they exist under the assumption that the ambient gas density decays with a given power of the radius. The non-self-similar situation, occurring for uniform density, is also considered. Cited in 12 Documents MSC: 76N15 Gas dynamics (general theory) 76L05 Shock waves and blast waves in fluid mechanics 80A20 Heat and mass transfer, heat flow (MSC2010) Keywords:ambient gas; ideal gas; sherical waves; shock wave; heat wave; Lie group symmetry; self-similar solutions; non-self-similar situation PDFBibTeX XMLCite \textit{P. Reinicke} and \textit{J. Meyer-ter-Vehn}, Phys. Fluids, A 3, No. 7, 1807--1818 (1991; Zbl 0745.76071) Full Text: DOI Link References: [1] DOI: 10.1098/rspa.1950.0049 · Zbl 0036.26404 · doi:10.1098/rspa.1950.0049 [2] DOI: 10.1063/1.1724332 · Zbl 0081.41601 · doi:10.1063/1.1724332 [3] DOI: 10.1063/1.865533 · Zbl 0626.76003 · doi:10.1063/1.865533 [4] Meyer-ter-Vehn J., Z. Naturforsch. 37 pp 955– (1982) [5] DOI: 10.1038/239139a0 · doi:10.1038/239139a0 [6] DOI: 10.1088/0741-3335/31/10/010 · doi:10.1088/0741-3335/31/10/010 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.