Stability condition for strong shock waves in the problem of flow around an infinite plane wedge

We consider the thermodynamical equilibrium state flow of an inviscid non-heat-conducting gas flowing around a plane infinite wedge, and study the stationary solution to this problem–the so-called strong shock wave; the flow behind the shock front is subsonic. We find the solution to the linear anal...

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Bibliographic Details
Published in:Nonlinear analysis. Hybrid systems 2008-03, Vol.2 (1), p.1-17
Main Authors: Blokhin, A.M., Tkachev, D.L., Pashinin, Yu.Yu
Format: Article
Language:English
Subjects:
Generalized solution
Lyapunov asymptotical stability
Plane wedge
Strong shock wave
Uniform Lopatinsky condition
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Summary:We consider the thermodynamical equilibrium state flow of an inviscid non-heat-conducting gas flowing around a plane infinite wedge, and study the stationary solution to this problem–the so-called strong shock wave; the flow behind the shock front is subsonic. We find the solution to the linear analog of the original mixed problem, prove that the solution trace on the shock wave is the superposition of the direct and reflected waves, and (the main point) justify the Lyapunov asymptotical stability of the strong shock wave provided that the uniform Lopatinsky condition is fulfilled. The initial data have a compact support, and the solvability conditions occur.
ISSN:1751-570X
DOI:10.1016/j.nahs.2006.10.012