Formation of δ-Shocks and Vacuum States in the Vanishing Pressure Limit of Solutions to the Euler Equations for Isentropic Fluids

By Gui-Qiang G. Chen, Hailiang Liu. SIAM Journal on Mathematical Analysis, 2003

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Interactions of delta shock waves for the transport equations with split delta functions (2009, neutral): “For the related work, we can see [1,3,5,8,10,14] and the references cited therein.”
Formation of delta shocks and vacuum states in the vanishing pressure limit of Riemann solutions to the perturbed Aw-Rascle model (2010, background): “In [11], Chen and Liu considered the Euler equations of isentropic fluids with the perturbed pressure term as follows: { ρt + (ρu)x = 0, (ρu)t + ( ρu2 + εp(ρ))x = 0, (1.”
Concentration and cavitation in the vanishing pressure limit of solutions to the Euler equations for nonisentropic fluids (2004, methodology): “which is different from the situation for isentropic flow [ 11 ].”
Singular solutions of a fully nonlinear 2 × 2 system of conservation laws (2011, background): “In the last few years, interest in the topic has grown, and a sample of results may be found in [4, 10, 14, 16, 19, 20, 21, 25, 27, 28, 31, 36, 37, 39].”