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  1. Proceedings of the Steklov Institute of Mathematics
  2. Proceedings of the Steklov Institute of Mathematics : Volume 281
  3. Proceedings of the Steklov Institute of Mathematics : Volume 281, Issue 1, July 2013
  4. On the acceleration of shock waves and concentration of energy
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Proceedings of the Steklov Institute of Mathematics : Volume 296
Proceedings of the Steklov Institute of Mathematics : Volume 295
Proceedings of the Steklov Institute of Mathematics : Volume 294
Proceedings of the Steklov Institute of Mathematics : Volume 293
Proceedings of the Steklov Institute of Mathematics : Volume 292
Proceedings of the Steklov Institute of Mathematics : Volume 291
Proceedings of the Steklov Institute of Mathematics : Volume 290
Proceedings of the Steklov Institute of Mathematics : Volume 289
Proceedings of the Steklov Institute of Mathematics : Volume 288
Proceedings of the Steklov Institute of Mathematics : Volume 287
Proceedings of the Steklov Institute of Mathematics : Volume 286
Proceedings of the Steklov Institute of Mathematics : Volume 285
Proceedings of the Steklov Institute of Mathematics : Volume 284
Proceedings of the Steklov Institute of Mathematics : Volume 283
Proceedings of the Steklov Institute of Mathematics : Volume 282
Proceedings of the Steklov Institute of Mathematics : Volume 281
Proceedings of the Steklov Institute of Mathematics : Volume 281, Issue 1, July 2013
Andrei Gennad’evich Kulikovskii : On the occasion of his 80th birthday
Cauchy problem in a scale of Banach spaces
Numerical and experimental simulation of wave formation during explosion welding
A new shimmy model
Mathematical modeling of shock-wave processes under gas solid boundary interaction
Stability of a flame front in a divergent flow
Kinetic equation method for problems of viscous gas dynamics with rapidly oscillating density distributions
Hyperbolic submodels of an incompressible viscoelastic Maxwell medium
Ball on a viscoelastic plane
Effect of crystallization, heat exchange, and viscous dissipation on the dynamics of extrusive eruptions
Influence of electromagnetic fields on the evolution of initially homogeneous and isotropic universe
Coupled-mode flutter of an elastic plate in a gas flow with a boundary layer
On the acceleration of shock waves and concentration of energy
Homogenization and dispersion effects in the problem of propagation of waves generated by a localized source
Classification of the types of instability of vertical flows in geothermal systems
Collision of a solar wind shock wave with the Earth’s bow shock. Wave flow pattern
Nonstationary solutions of a generalized Korteweg-de Vries-Burgers equation
Proceedings of the Steklov Institute of Mathematics : Volume 281, Issue 1, Supplement,June 2013
Proceedings of the Steklov Institute of Mathematics : Volume 280
Proceedings of the Steklov Institute of Mathematics : Volume 279
Proceedings of the Steklov Institute of Mathematics : Volume 278
Proceedings of the Steklov Institute of Mathematics : Volume 277
Proceedings of the Steklov Institute of Mathematics : Volume 276
Proceedings of the Steklov Institute of Mathematics : Volume 275
Proceedings of the Steklov Institute of Mathematics : Volume 274
Proceedings of the Steklov Institute of Mathematics : Volume 273
Proceedings of the Steklov Institute of Mathematics : Volume 272
Proceedings of the Steklov Institute of Mathematics : Volume 271
Proceedings of the Steklov Institute of Mathematics : Volume 270
Proceedings of the Steklov Institute of Mathematics : Volume 269
Proceedings of the Steklov Institute of Mathematics : Volume 268
Proceedings of the Steklov Institute of Mathematics : Volume 267
Proceedings of the Steklov Institute of Mathematics : Volume 266
Proceedings of the Steklov Institute of Mathematics : Volume 265
Proceedings of the Steklov Institute of Mathematics : Volume 264
Proceedings of the Steklov Institute of Mathematics : Volume 263
Proceedings of the Steklov Institute of Mathematics : Volume 262
Proceedings of the Steklov Institute of Mathematics : Volume 261
Proceedings of the Steklov Institute of Mathematics : Volume 260
Proceedings of the Steklov Institute of Mathematics : Volume 259
Proceedings of the Steklov Institute of Mathematics : Volume 258
Proceedings of the Steklov Institute of Mathematics : Volume 257
Proceedings of the Steklov Institute of Mathematics : Volume 256
Proceedings of the Steklov Institute of Mathematics : Volume 255
Proceedings of the Steklov Institute of Mathematics : Volume 254
Proceedings of the Steklov Institute of Mathematics : Volume 253
Proceedings of the Steklov Institute of Mathematics : Volume 252

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On the acceleration of shock waves and concentration of energy

Content Provider Springer Nature Link
Author Golubyatnikov, A. N.
Copyright Year 2013
Abstract 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.
Starting Page 153
Ending Page 160
Page Count 8
File Format PDF
ISSN 00815438
Journal Proceedings of the Steklov Institute of Mathematics
Volume Number 281
Issue Number 1
e-ISSN 15318605
Language English
Publisher Springer US
Publisher Date 2013-07-26
Publisher Place Boston
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Mathematics
Content Type Text
Resource Type Article
Subject Mathematics
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