Delta-shock wave type solution of hyperbolic systems of conservation laws

Danilov, V.; Shelkovich, V.

doi:10.1090/S0033-569X-05-00961-8

Authors: V. G. Danilov and V. M. Shelkovich
Journal: Quart. Appl. Math. 63 (2005), 401-427
MSC (2000): Primary 35L65; Secondary 35L67, 76L05
DOI: https://doi.org/10.1090/S0033-569X-05-00961-8
Published electronically: August 17, 2005
MathSciNet review: 2169026
Full-text PDF Free Access

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Abstract: For two classes of hyperbolic systems of conservation laws new definitions of a $\delta$-shock wave type solution are introduced. These two definitions give natural generalizations of the classical definition of the weak solutions. It is relevant to the notion of $\delta$-shocks. The weak asymptotics method developed by the authors is used to describe the propagation of $\delta$-shock waves to the three types of systems of conservation laws and derive the corresponding Rankine–Hugoniot conditions for $\delta$-shocks.

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