naa a22 4500 510812414 CHVBK 20180411083449.0 cr unu---uuuuu 180411e20130701xx s 000 0 eng 10.1134/S0081543813040135 doi (NATIONALLICENCE)springer-10.1134/S0081543813040135 Golubyatnikov A. Faculty of Mechanics and Mathematics, Moscow State University, 119991, Moscow, Russia aut On the acceleration of shock waves and concentration of energy [Elektronische Daten] [A. Golubyatnikov] By a series of simple examples related to exact solutions of problems in gas dynamics and magnetohydrodynamics, possible mechanisms of acceleration of shock waves and concentration of energy are elucidated. The acceleration of a shock wave is investigated in the problem of motion of a plane piston at a constant velocity in the case when the initial density of the medium drops in the presence of constant counterpressure. It is shown that in this situation a "blow-up” regime is induced by a shock wave going to infinity in finite time even for limited work of the piston. A simple spherically symmetric solution with a converging shock wave is constructed and shown to lead to the concentration of energy. A general method for solving one-dimensional non-self-similar problems related to matching the equilibrium state to a motion with homogeneous deformation on a shock wave is discussed; this method leads to a solution in quadratures. Pleiades Publishing, Ltd., 2013 Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 281/1(2013-07-01), 153-160 0081-5438 281:1<153 2013 281 11501 https://doi.org/10.1134/S0081543813040135 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813040135 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Golubyatnikov A. Faculty of Mechanics and Mathematics, Moscow State University, 119991, Moscow, Russia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics Springer US; http://www.springer-ny.com 281/1(2013-07-01), 153-160 0081-5438 281:1<153 2013 281 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer