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

Two‐phase states of the generalized van der Waals gas: Conditions of absolute and neutral shock wave stability

“…In a number of works [3][4][5][6][7][8][9][10][11][12], this hypothesis got its confirmation on the linear level, but its justification for quasilinear problem statement is yet ahead of us. In conclusion, let us note that we account for the nonuniformity of the matter that is necessary to study the interactions of, for example, aircrafts with the surrounding medium under the supersonic flying speeds.…”

Courant-Friedrichs' Hypothesis and Stability of the Weak Shock Wave Satisfying the Lopatinski Condition

“…The Courant-Friedrichs' hypothesis was verified in [4][5][6][7] (but this conclusion was based only on some qualitative reasons). A strict mathematical justification (and this is very important) of this statement for the linearized problem appeared in recent years in [8][9][10][11][12]. Briefly speaking, it was shown in [8][9][10][11][12] that in the case of a strong shock wave (for compactly supported initial data!)…”

“…A strict mathematical justification (and this is very important) of this statement for the linearized problem appeared in recent years in [8][9][10][11][12]. Briefly speaking, it was shown in [8][9][10][11][12] that in the case of a strong shock wave (for compactly supported initial data!) the perturbation arrives to the wedge's vertex as time increases having the growth r  ( 0   ) or a logarithmic growth in space variables, and this causes instability of the steady-state solution under consideration.…”

Justification of the Courant–Friedrich's hypothesis in the case of a weak shock. Part I. Presentation of solution to linear problem

“…Firstly, in [14] the well-posedness of the linearized initial-boundary value problem has been proved at least for the case of small angles at the wedge's vertex. Secondly, in [15][16][17] an implicit generalized solution of the linearized problem has been found for compactly supported initial data and under the fulfillment of an additional integral condition at the wedge's vertex (again the angle at the wedge's vertex is assumed small enough). For the first time one has managed to realize that the boundary singularity influences on the character of the solution itself.…”