A complete solution to the local theory of the shock wave reflection at an inclined wall has been obtained for the first time in two particular regions. One is the region near the Mach stem confluence S point with the wall and the other in the vicinity of the triple point T of an irregular shock-wave configuration. The correct lines of regular-irregular transitions have been established for the self-similar reflection problem in shock tubes. The solutions for all shock-fronts geometry have been obtained in the vicinity of the triple point, which are in agreement with the results of experimental measurements. In all the region of interaction the backward-reflected shock waves have been obtained for incident waves of arbitrary intensity. It has been formulated the hypothesis concerning the regular-irregular transition of weak shock waves, as a result of disintegration of an arbitrary discontinuity formed at the terminal stage of regular reflection.
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