Interactions of delta shock waves in a pressureless hydrodynamic model

References

• Piccoli B, Tosin A, Zanella M. Model-based assessment of the impact of driver-assist vehicles using kinetic theory. Z Angew Math Phys. 2020;71:152.
   Web of Science ®Google Scholar
• Dimarco G, Tosin A. The Aw-Rascle traffic model: enskog-type kinetic derivation and generalisations. J Statist Phys. 2020;178:178–210.
   Web of Science ®Google Scholar
• Pareschi L, Toscani G, Tosin A, et al. Hydrodynamic models of preference formation in multi-agent societies. J Nonlinear Sci. 2019;29:2761–2796.
   Web of Science ®Google Scholar
• Nedeljkov M, Oberguggenberger M. Interactions of delta shock waves in a strictly hyperbolic system of conservation laws. J Math Anal Appl. 2008;344:1143–1157.
   Web of Science ®Google Scholar
• Nedeljkov M. Singular shock waves in interactions. Q Appl Math. 2008;66:281–302.
   Web of Science ®Google Scholar
• Nedeljkov M. Shadow waves: entropies and interactions for delta and singular shocks. Arch Rational Mech Anal. 2010;197:489–537.
   Web of Science ®Google Scholar
• De la Cruz R, Santos M, Abreu E. Interaction of delta shock waves for a nonsymmetric Keyfitz–Kranzer system of conservation laws. Monatsh Math. 2021;194:737–766.
   Web of Science ®Google Scholar
• Guo L, Zhang Y, Yin G. Interaction of delta shock waves for the Chaplygin gas equation with split delta functions. J Math Anal Appl. 2014;410:190–201.
   Web of Science ®Google Scholar
• Guo L, Zhang Y, Yin G. Interactions of delta shock waves for the relativistic Chaplygin Euler equations with split delta functions. Math Meth Appl Sci. 2015;38:2132–2148.
   Web of Science ®Google Scholar
• Sen A, Raja Sekhar T, Sharma VD. Wave interactions and stability of the Riemann solution for a strictly hyperbolic system of conservation laws. Q Appl Math. 2017;75:539–554.
   Web of Science ®Google Scholar
• Sen A, Raja Sekhar T. Delta shock wave and wave interactions in a thin film of a perfectly soluble anti-surfactant solution. Commun Pure Appl Anal. 2020;19:2641–2653.
   Web of Science ®Google Scholar
• Shen C, Sun M. Interactions of delta shock waves for the transport equations with split delta functions. J Math Anal Appl. 2009;351:747–755.
   Web of Science ®Google Scholar
• Shen C, Sun M. Stability of the Riemann solutions for a nonstrictly hyperbolic system of conservation laws. Nonlinear Anal: TMA. 2010;73:3284–3294.
   Web of Science ®Google Scholar
• Sun M. Interactions of delta shock waves for the chromatography equations. Appl Math Lett. 2013;26:631–637.
   Web of Science ®Google Scholar
• Chen T, Jiang W, Li T. On the stability of the improved Aw–Rascle–Zhang model with Chaplygin pressure. Nonlinear Anal: RWA. 2021;62:103351.
   Web of Science ®Google Scholar
• Qu A, Wang Z. Stability of the Riemann solutions for a Chaplygin gas. J Math Anal Appl. 2014;409:347–361.
   Web of Science ®Google Scholar
• Sun M. Singular solutions to the Riemann problem for a macroscopic production model. Z Angew Math Mech. 2017;97:916–931.
   Web of Science ®Google Scholar
• Zhang Y, Zhang Y. The Riemann problem and interaction of waves in two-dimensional steady zero-pressure aiabatic flow. Int J Non-linear Mech. 2018;104:100–108.
   Web of Science ®Google Scholar
• Zhang Y, Zhang Y. Riemann problem and wave interactions for a class of strictly hyperbolic systems of conservation laws. Bull Braz Math Soc, New Ser. 2020;51:1017–1040.
   Google Scholar
• Lai G, Sheng W. Elementary wave interactions to the compressible Euler equations for Chaplygin gas in two dimensions. SIAM J Appl Math. 2016;76:2218–2242.
   Web of Science ®Google Scholar
• Lai G, Sheng W, Zheng Y. Simple waves and pressure delta waves for a Chaplygin gas in multi-dimensions. Discrete Contin Dyn Syst. 2011;31:489–523.
   Web of Science ®Google Scholar
• Sun M. Interactions of elementary waves for the Aw–Rascle model. SIAM J Appl Math. 2009;69:1542–1558.
   Web of Science ®Google Scholar
• Wang Z, Zhang Q. The Riemann problem with delta initial data for the one-dimensional Chaplygin gas equations. Acta Math Sci. 2012;32B:825–841.
   Google Scholar
• Yang H, Sun W. The Riemann problem with delta initial data for a class of coupled hyperbolic systems of conservation laws. Nonlinear Anal TMA. 2007;67:3041–3049.
   Web of Science ®Google Scholar
• Paiva A. Interaction of dirac δ−waves in the nonlinear Klein–Gordon equation. J Differ Equations. 2021;270:1196–1217.
   Web of Science ®Google Scholar
• Sarrico COR, Paiva A. Delta shock waves in the shallow water system. J Dyn Differ Equations. 2018;30:1187–1198.
   Web of Science ®Google Scholar
• Sarrico COR, Paiva A. Distributions as initial values in a triangular hyperbolic system of conservation laws. Proc R Soc Edinburgh, Section A: Mathematics. 2020;150:2757–2775.
   Web of Science ®Google Scholar
• Chen GQ, Liu H. Formation of δ-shocks and vacuum states in the vanishing pressure limit of solutions to the Euler equations for isentropic fluids. SIAM J Math Anal. 2003;34:925–938.
   Web of Science ®Google Scholar
• Li H, Shao Z. Delta shocks and vacuum states in vanishing pressure limits of solutions to the relativistic Euler equations for generalized Chaplygin gas. Commun Pure Appl Anal. 2016;15:2373–2400.
   Web of Science ®Google Scholar
• Shao Z. Delta shocks and vacuum states for the isentropic magnetogasdynamics equations for Chaplygin gas as pressure and magnetic field vanish. Anal Math Phys. 2022;12:85.
   Web of Science ®Google Scholar
• Shen C, Sun M. Exact Riemann solutions for the drift-flux equations of two-phase flow under gravity. J Differ Equations. 2022;314:1–55.
   Web of Science ®Google Scholar
• Shen C, Sun M. Formation of vacuum state and delta shock wave for the relativistic Euler system for polytropic gas with the varying γ-law. Z Angew Math Phys. 2022;73:69.
   Web of Science ®Google Scholar
• Sheng S, Shao Z. Concentration of mass in the pressureless limit of the Euler equations of one-dimensional compressible fluid flow. Nonlinear Anal RWA. 2020;52:103039.
   Web of Science ®Google Scholar
• Sheng W, Zhang T. The Riemann problem for the transportation equations in gas dynamics. Mem Amer Math Soc. 1999;137(N654):1–77.
   Google Scholar
• Sun M. Concentration and cavitation phenomena of Riemann solutions for the isentropic Euler system with the logarithmic equation of state. Nonlinear Anal: RWA. 2020;53:103068.
   Web of Science ®Google Scholar
• Yang H, Zhang Y. New development of delta shock waves and its applications in systems of conservation laws. J Differ Equations. 2012;252:5951–5993.
   Web of Science ®Google Scholar
• Abreu E, De la Cruz R, Lambert W. Riemann problem and delta-shock solutions for a Keyfitz–Kranzer system with a forcing term. J Math Anal Appl. 2021;502:125267.
   Web of Science ®Google Scholar
• Danilov VG, Shelkovich VM. Dynamics of propagation and interaction of δ-shock waves in conservation law systems. J Differ Equations. 2005;211:333–381.
   Web of Science ®Google Scholar
• Kalisch H, Mitrovic D. Singular solutions of a fully nonlinear 2×2 system of conservation laws. Proc Edinburgh Math Soc. 2012;55:711–729.
   Web of Science ®Google Scholar
• Kalisch H, Mitrovic D, Teyekpiti V. Existence and uniqueness of singular solutions for a conservation law arising in magnetohydrodynamics. Nonlinearity. 2018;31:5463–5483.
   Web of Science ®Google Scholar
• Nilsson B, Shelkovich VM. Mass, momentum and energy conservation laws in zero-pressure gas dynamics and delta-shocks. Appl Anal. 2011;90:1677–1689.
   Web of Science ®Google Scholar
• Ruzicic S, Nedeljkov M. Shadow wave tracking procedure and initial data problem for pressureless gas model. Acta Appl Math. 2021;171:10.
   Web of Science ®Google Scholar