Linearization of the Riemann problem for a triangular system of conservation laws and delta shock wave formation process
Darko Mitrovic, Vladimir Danilov, Velibor Bojkovic
Abstract: We generalize procedure from [a] on the case of more general triangular system of conservation laws arising from so called generalized pressureless gas dynamics. Using the weak asymptotic method, more precisely nonlinear superposition law [b], we approximate the nonlinear system by a linear one. Then, we can use usual method of characteristics to find approximate solution to the original system. As a consequence, we shall see how delta shock wave naturally arises along the characteristics.
[a] D.Mitrovic, J.Susic: Global in time solution to Hopf
equation and application to a non-strictly hyperbolic
system of conservation laws,
Electronic J. of Differential Equations,
Vol. 2007 (2007) No. 114, 1–22.
[b] V.G.Danilov, D.Mitrovic: Weak asymptotic of shock wave formation process, Journal of Nonlinear Analysis – Theory, Methods and Applications, Vol. 61 (2005) 613–635.