EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 17 (2022) Math. Model. Nat. Phenom., 17 (2022) 26 References
Open Access
Issue
Math. Model. Nat. Phenom.
Volume 17, 2022
Article Number 26
Number of page(s) 23
DOI https://doi.org/10.1051/mmnp/2022029
Published online 04 August 2022
  1. E. Abreu, R. De la Cruz and W. Lambert, Riemann problem and delta-shock solutions for a Keyfitz-Kranzer system with a forcing term. J. Math. Anal. Appl. 502 (2021) 125267. [CrossRef] [Google Scholar]
  2. A. Aggarwal, G. Vaidya and G.D.V. Gowda, Positivity-preserving numerical scheme for hyperbolic systems with delta-shock solutions and its convergence analysis. Z. Angew. Math. Phys. 72 (2021) 165. [CrossRef] [Google Scholar]
  3. D. Armbruster and M. Wienke, Kinetic models and intrinsic timescales: simulation comparison for a 2nd order queueing model. Kinetic Related Models 12 (2019) 177–193. [CrossRef] [MathSciNet] [Google Scholar]
  4. D. Armbruster, D. Marthaler and C. Ringhofer, Kinetic and fluid model hierarchies for supply chains. Multiscale Model. Simul. 2 (2013) 43–61. [Google Scholar]
  5. D. Armbruster, P. Degond and C. Ringhofer, A model for the dynamics of large queuing networks and supply chains. SIAM J. Appl. Math. 66 (2006) 896–920. [Google Scholar]
  6. F. Betancourt, R. Burger, C. Chalons, S. Diehl and S. Faras, A random sampling approach for a family of Temple-class systems of conservation laws. Numer. Math. 138 (2018) 37–73. [CrossRef] [MathSciNet] [Google Scholar]
  7. F. Bouchut, On zero pressure gas dynamics, in vol. 22 of Advances in Kinetic Theory and Computing, Ser. Adv. Math. Appl. Sci. World Sci. Publishing, River Edge, NJ (1994) 171–190. [Google Scholar]
  8. G.Q. Chen and H. Liu, 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. 34 (2003) 925–938. [CrossRef] [MathSciNet] [Google Scholar]
  9. V.G. Danilov and V.M. Shelkovich, Dynamics of propagation and interaction of δ-shock waves in conservation law systems. J. Differ. Equ. 211 (2005) 333–381. [CrossRef] [Google Scholar]
  10. L. Forestier-Coste, S. Gottlich and M. Herty, Data-fitted second-order macroscopic production models. SIAM J. Appl. Math. 75 (2015) 999–1014. [CrossRef] [MathSciNet] [Google Scholar]
  11. L. Guo, T. Li and G. Yin, The vanishing pressure limits of Riemann solutions to the Chaplygin gas equations with a source term. Commun. Pure Appl. Anal. 16 (2017) 295–309. [CrossRef] [MathSciNet] [Google Scholar]
  12. L. Guo, T. Li and G. Yin, The transition of Riemann solutions of the modified Chaplygin gas equations with friction to the solutions of the Chaplygin gas equations. Z. Angew. Math. Mech. 102 (2022) e201800064. [Google Scholar]
  13. S.T. Hilden, H.M. Nilsen and X. Raynaud, Study of the well-posedness of models for the inaccessible pore volume in polymer flooding. Transport in Porous Media 114 (2016) 65–86. [CrossRef] [MathSciNet] [Google Scholar]
  14. F. Huang and Z. Wang, Well-posedness for pressureless flow. Comm. Math. Phys. 222 (2001) 117–146. [CrossRef] [MathSciNet] [Google Scholar]
  15. M. Ibrahim, F. Liu and S. Liu, Concentration of mass in the pressureless limit of Euler equations for power law. Nonlinear Analysis: RWA 47 (2019) 224–235. [CrossRef] [Google Scholar]
  16. H. Kalisch and D. Mitrovic, Singular solutions of a fully nonlinear 2 x 2 system of conservation laws. Proc. Edinburgh Math. Soc. 55 (2012) 711–729. [CrossRef] [MathSciNet] [Google Scholar]
  17. H. Kalisch, D. Mitrovic and V. Teyekpiti, Existence and uniqueness of singular solutions for a conservation law arising in magnetohydrodynamics. Nonlinearity 31 (2018) 5463–5483. [CrossRef] [MathSciNet] [Google Scholar]
  18. H. Kalisch, D Mitrovic and V. Teyekpiti, Delta shock waves in shallow water flow. Phys. Lett. A 381 (2017) 1138–1144. [CrossRef] [MathSciNet] [Google Scholar]
  19. D.M. Lu, H.C. Simpson and A. Gilchrist, The application of split-coefficient matrix method to transient two phase flows. Int. J. Num. Meth. Heat Fluid flow 6 (1996) 63–76. [Google Scholar]
  20. M. Mazzotti, A. Tarafder, J. Cornel, F. Gritti and G. Guiochon, Experimental evidence of a delta-shock in nonlinear chromatography. J. Chromatogr. A 1217 (2010) 2002–2012. [CrossRef] [Google Scholar]
  21. T. Minhajul and R. Sekhar, Nonlinear wave interactions in a macroscopic production model. Acta Math. Sci. Ser. B 41 (2021) 764–780. [CrossRef] [MathSciNet] [Google Scholar]
  22. D. Mitrovic and M. Nedeljkov, Delta-shock waves as a limit of shock waves. J. Hyperbolic Differ. Equ. 4 (2007) 629–653. [CrossRef] [Google Scholar]
  23. M. Nedeljkov, Shadow waves: entropies and interactions for delta and singular shocks. Arch. Rational Mech. Anal. 197 (2010) 489–537. [CrossRef] [MathSciNet] [Google Scholar]
  24. A. Qu, H. Yuan and Q. Zhao, High Mach number limit of one-dimensional piston problem for non-isentropic compressible Euler equations: polytropic gas. J. Math. Phys. 61 (2020) 011507. [CrossRef] [MathSciNet] [Google Scholar]
  25. C.O.R. Sarrico and A. Paiva, Delta shock waves in the shallow water system. J. Dyn. Differ. Equ. 30 (2018) 1187–1198. [CrossRef] [Google Scholar]
  26. A. Sen and T. Raja Sekhar, The limiting behavior of the Riemann solution to the isentropic Euler system for the logarithmic equation of state with a source term. Math. Methods Appl. Sci. 44 (2021) 7207–7207. [CrossRef] [MathSciNet] [Google Scholar]
  27. A. Sen and T. Raja Sekhar, Delta shock wave as self-similar viscosity limit for a strictly hyperbolic system of conservation laws. J. Math. Phys. 60 (2019) 051510. [CrossRef] [MathSciNet] [Google Scholar]
  28. A. Sen and T. Raja Sekhar, Delta shock wave and wave interactions in a thin film of a perfectly soluble anti-surfactant solution. Commun. Pure Appl. Anal. 19 (2020) 2641–2653. [CrossRef] [MathSciNet] [Google Scholar]
  29. A. Sen, T. Raja Sekhar and D. Zeidan, Stability of the Riemann solution for a 2 x 2 strictly hyperbolic system of conservation laws. Sadhana 44 (2019) 228. [CrossRef] [Google Scholar]
  30. C. Shen and M. Sun, Formation of delta shocks and vacuum states in the vanishing pressure limit of Riemann solutions to the perturbed Aw-Rascle model. J. Differ. Equ. 249 (2010) 3024–3051. [CrossRef] [MathSciNet] [Google Scholar]
  31. C. Shen and M. Sun, Exact Riemann solutions for the drift-flux equations of two-phase flow under gravity. J. Differ. Equ. 314 (2022) 1–55. [CrossRef] [Google Scholar]
  32. W. Sheng and T. Zhang, The Riemann problem for the transportation equations in gas dynamics. Mem. Amer. Math. Soc. 137 (N654) (1999) 1–77. [Google Scholar]
  33. W. Sheng, G. Wang and G. Yin, Delta wave and vacuum state for generalized Chaplygin gas dynamics system as pressure vanishes. Nonlinear Analysis: RWA 22 (2015) 115–128. [CrossRef] [Google Scholar]
  34. S. Sheng and Z. Shao, The vanishing adiabatic exponent limits of Riemann solutions to the isentropic Euler equations for power law with a Coulomb-like friction term. J. Math. Phys. 60 (2019) 101504. [CrossRef] [MathSciNet] [Google Scholar]
  35. S. Sheng and Z. Shao, The limits of Riemann solutions to Euler equations of compressible fluid flow with a source term. J. Engineering Math. 125 (2020) 1–22. [CrossRef] [Google Scholar]
  36. S. Sheng and Z. Shao, Concentration of mass in the pressureless limit of the Euler equations of one-dimensional compressible fluid flow. Nonlinear Analysis: RWA 52 (2020) 103039. [CrossRef] [Google Scholar]
  37. S. Sil and T. Raja Sekhar, Nonlocally related systems, nonlocal symmetry reductions and exact solutions for one-dimensional macroscopic production model. Eur. Phys. J. Plus 135 (2020) 514. [CrossRef] [Google Scholar]
  38. S. Sil and T. Raja Sekhar, Nonclassical symmetry analysis, conservation laws of one-dimensional macroscopic production model and evolution of nonlinear waves. J. Math. Anal. Appl. 497 (2021) 124847. [CrossRef] [Google Scholar]
  39. M. Sun, Singular solutions to the Riemann problem for a macroscopic production model. Z. Angew. Math. Mech. 97 (2017) 916–931. [CrossRef] [MathSciNet] [Google Scholar]
  40. M. Sun, The limits of Riemann solutions to the simplified pressureless Euler system with flux approximation. Math. Methods Appl. Sci. 41 (2018) 4528–4548. [CrossRef] [MathSciNet] [Google Scholar]
  41. M. Sun, Concentration and cavitation phenomena of Riemann solutions for the isentropic Euler system with the logarithmic equation of state. Nonlinear Analysis: RWA 53 (2020) 103068. [CrossRef] [Google Scholar]
  42. B. Temple, Systems of conservation laws with invariant submanifolds. Trans. Am. Math. Soc. 280 (1983) 781–795. [CrossRef] [Google Scholar]
  43. P. Wang and C. Shen, The perturbed Riemann problem for a macroscopic production model with Chaplygin gas. Bull. Malays. Math. Sci. Soc. 44 (2021) 1195–1214. [CrossRef] [MathSciNet] [Google Scholar]
  44. H. Yang and J. Liu, Delta-shocks and vacuums in zero-pressure gas dynamics by the flux approximation. Science China Math. 58 (2015) 2329–2346. [CrossRef] [MathSciNet] [Google Scholar]
  45. H. Yang and Y. Zhang, Pressure and flux-approximation to the isentropic relativistic Euler equations for the modified Chaplygin gas. J. Math. Phys. 60 (2019) 071502. [CrossRef] [MathSciNet] [Google Scholar]
  46. Q. Zhang, Concentration in the flux approximation limit of Riemann solutions to the extended Chaplygin gas equations with friction. J. Math. Phys. 60 (2019) 101508. [CrossRef] [MathSciNet] [Google Scholar]
  47. Y. Zhang and M. Sun, The intrinsic phenomena of concentration and cavitation on the Riemann solutions for the perturbed macroscopic production model. Math. Meth. Appl. Sci. 45 (2022) 864–881. [CrossRef] [Google Scholar]
  48. Y. Zhang, Y. Zhang and J. Wang, Concentration in the zero-exponent limit of solutions to the isentropic Euler equations for extended Chaplygin gas. Asymptotic Anal. 122 (2021) 35–67. [CrossRef] [MathSciNet] [Google Scholar]
  49. Y. Zhang, Y. Zhang and J. Wang, Zero-exponent limit to the extended Chaplygin gas equations with friction. Bull. Malays. Math. Sci. Soc. 44 (2021) 3571–3599. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.