THE EXISTENCE AND UNIQUENESS OF SELF-SIMILAR SOLUTIONS INVOLVING JOUGUET POINTS ON THE SHOCK ADIABATIC CURVE

The self-similar solutions of one-dimensional unsteady equations of th e hyperbolic type which express the conservation laws are considered. A number of special features have been revealed [1-4] in the non-linea r theory of elasticity: the absence of uniqueness, the absence of a co ntinuous dependence of a solution on the parameters and rapid changeov ers of a wave of one type with the emission of a wave of another type. It has been shown that all of these phenomena have a common character and are associated with the presence of a ''foreign'' Jouguet point o n the shock adiabat. The velocity of a shock wave of a certain type at this point is equal to the characteristic velocity downstream of a sh ock wave of another neighbouring and slower type. Hence, in the case o f hyperbolic systems, which express the conservation laws, the possibi lity exists of judging the most important properties of selfsimilar so lutions as a whole using certain properties of the shock adiabats. (C) 1996 Elsevier Science Ltd.