$L^\infty$-Stability of Continuous Shock Waves in a Radiating Gas Model

Masashi Ohnawa

doi:10.1137/130935252

$L^\infty$-Stability of Continuous Shock Waves in a Radiating Gas Model

SIAM Journal on Mathematical Analysis ◽

10.1137/130935252 ◽

2014 ◽

Vol 46 (3) ◽

pp. 2136-2159 ◽

Cited By ~ 5

Author(s):

Masashi Ohnawa

Keyword(s):

Shock Waves ◽

Continuous Shock

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Continuous shock waves in an ideal radiating gas

USSR Computational Mathematics and Mathematical Physics ◽

10.1016/0041-5553(75)90213-x ◽

1975 ◽

Vol 15 (6) ◽

pp. 177-184

Author(s):

V.M. Borisov

Keyword(s):

Shock Waves ◽

Continuous Shock

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Investigation of shock-wave deformation history from recovered structure

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100143754 ◽

1986 ◽

Vol 44 ◽

pp. 434-435

Author(s):

M.A. Mogilevsky ◽

L.S. Bushnev

Keyword(s):

Shock Wave ◽

Plastic Deformation ◽

Dislocation Density ◽

Shock Waves ◽

Shock Front ◽

Single Crystals ◽

Residual Deformation ◽

Deformation Structure ◽

Deformation History ◽

Deformation Velocity

Single crystals of Al were loaded by 15 to 40 GPa shock waves at 77 K with a pulse duration of 1.0 to 0.5 μs and a residual deformation of ∼1%. The analysis of deformation structure peculiarities allows the deformation history to be re-established.After a 20 to 40 GPa loading the dislocation density in the recovered samples was about 1010 cm-2. By measuring the thickness of the 40 GPa shock front in Al, a plastic deformation velocity of 1.07 x 108 s-1 is obtained, from where the moving dislocation density at the front is 7 x 1010 cm-2. A very small part of dislocations moves during the whole time of compression, i.e. a total dislocation density at the front must be in excess of this value by one or two orders. Consequently, due to extremely high stresses, at the front there exists a very unstable structure which is rearranged later with a noticeable decrease in dislocation density.

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