Study of the stability in the problem on flowing around a wedge. The case of strong wave |
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Authors: | AM Blokhin DL Tkachev |
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Institution: | a Institute of Mathematics, Novosibirsk 630090, Russia b Novosibirsk State University, Novosibirsk 630090, Russia |
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Abstract: | We consider the flow of an inviscid nonheatconducting gas in the thermodynamical equilibrium state 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 a solution to a mixed problem for a linear analog of the initial problem, prove that the solution trace on the shock wave is the superposition of direct and reflected waves, and, the main point, justify the Lyapunov asymptotical stability of the strong shock wave provided that the angle at the wedge vertex is small, the uniform Lopatinsky condition is fulfilled, the initial data have a compact support, and the solvability conditions take place if needed (their number depends on the class in which the generalized solution is found). |
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Keywords: | Infinite plane wedge Strong shock wave Generalized solution Uniform Lopatinsky condition Lyapunov asymptotical stability |
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