Abstract
The system of equations of 2-D pressure free gas dynamics is a nonstrictly hyperbolic system of conservation laws which has three coinciding characteristic fields and an incomplete set of eigenvectors. Due to these properties the shock waves develop strong singularities in the density which are of type of δ-functions on the surface. In this paper the notion of generalized solution in the sense of Radon measures is introduced and the generalization of Rankin-Hugoniot conditions is obtained. As a consequence it is shown that the system under consideration can not be reduced to single 2-D equation of Hamilton-Jacobi type in contrast to the 1-D case.
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Rykov, Y.G. (1999). The Propagation of Shock Waves in 2-D System of Pressureless Gas Dynamics. In: Jeltsch, R., Fey, M. (eds) Hyperbolic Problems: Theory, Numerics, Applications. International Series of Numerical Mathematics, vol 130. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8724-3_32
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DOI: https://doi.org/10.1007/978-3-0348-8724-3_32
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