Stability of a~supersonic flow about a~wedge with weak shock wave
Sbornik. Mathematics, Tome 200 (2009) no. 2, pp. 157-184
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It is known that the problem of finding the streamlines of a stationary supersonic flow
of a nonviscous nonheat-conducting gas in thermodynamical equilibrium past an infinite plane
wedge (with a sufficiently small angle at the vertex) in theory has two solutions: a strong shock wave solution (the velocity behind the front of the shock wave is subsonic) and a weak shock wave solution (the velocity behind the front of the shock wave is generally speaking supersonic). In the present paper it is shown
for a linear approximation to this problem that the weak shock wave solution is asymptotically stable in the sense of Lyapunov. Moreover, it is shown that for initial data with compact support the solution of the mixed linear problem converges in finite time to the zero solution. In the case of linear approximation these
results complete the verification of the well-known Courant-Friedrichs conjecture that the strong
shock wave solution is unstable, whereas the weak shock wave solution is asymptotically stable in the sense of Lyapunov.
Bibliography: 39 titles.
Keywords:
weak shock wave, asymptotic stability (in the sense of Lyapunov).
@article{SM_2009_200_2_a0,
author = {A. M. Blokhin and D. L. Tkachev},
title = {Stability of a~supersonic flow about a~wedge with weak shock wave},
journal = {Sbornik. Mathematics},
pages = {157--184},
publisher = {mathdoc},
volume = {200},
number = {2},
year = {2009},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SM_2009_200_2_a0/}
}
A. M. Blokhin; D. L. Tkachev. Stability of a~supersonic flow about a~wedge with weak shock wave. Sbornik. Mathematics, Tome 200 (2009) no. 2, pp. 157-184. http://geodesic.mathdoc.fr/item/SM_2009_200_2_a0/