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Interaction of a characteristic shock with a weak discontinuity in a non-ideal gas. (English) Zbl 1231.76132
Summary: The Lie group of point transformations, which leave the equations for plane and radially symmetric flows of a non-ideal gas invariant, are used to obtain an exact solution that exhibits space-time dependence. We consider the propagation of a weak discontinuity through a state, characterized by this solution. Further, the evolution of a characteristic shock and its interaction with the weak discontinuity are studied. The properties of reflected and transmitted waves and the jump in shock acceleration, influenced by the incident wave amplitude and the van der Waals excluded volume, are completely characterized, and certain observations are noted in respect of their contrasting behaviour.

MSC:
76L05 Shock waves and blast waves in fluid mechanics
35L60 First-order nonlinear hyperbolic equations
35A30 Geometric theory, characteristics, transformations in context of PDEs
35L67 Shocks and singularities for hyperbolic equations
76N15 Gas dynamics (general theory)
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