Free Access
Volume 54, Number 2, March-April 2020
Page(s) 465 - 492
Published online 18 February 2020
  1. D. Amadori and W. Shen, Front tracking approximations for slow erosion. Discrete Contin. Dyn. Syst. 32 (2012) 1481–1502. [CrossRef] [Google Scholar]
  2. D. Amadori and W. Shen, An integro-differential conservation law arising in a model of granular flow. J. Hyperbolic Differ. Equ. 9 (2012) 105–131. [CrossRef] [Google Scholar]
  3. G.R. Baker, R.E. Caflisch and M. Siegel, Singularity formation during Rayleigh-Taylor instability. J. Fluid Mech. 252 (1993) 51–75. [Google Scholar]
  4. R.E. Caflisch, Singularity formation for complex solutions of the 3D incompressible Euler equations. Phys. D 67 (1993) 1–18. [CrossRef] [Google Scholar]
  5. R.E. Caflisch, F. Gargano, M. Sammartino and V. Sciacca, Complex singularities and PDEs. Riv. Mat. Univ. Parma 6 (2015) 69–133. [Google Scholar]
  6. R.E. Caflisch, F. Gargano, M. Sammartino and V. Sciacca, Regularized Euler-α motion of an infinite array of vortex sheets. Boll. Unione Mat. Ital. 10 (2017) 113–141. [CrossRef] [Google Scholar]
  7. C. Canuto, M.Y. Hussaini, A. Quarteroni and T.A. Zang, Spectral Methods. Scientific Computation. Springer, Berlin (2007). [CrossRef] [Google Scholar]
  8. G.F. Carrier, M. Krook and C.E. Pearson, Function of a Complex Variable: Theory and Technique. McGraw–Hill, New York (1966). [Google Scholar]
  9. C. Chalons, P. Goatin and L. Villada, High-order numerical schemes for one-dimensional nonlocal conservation laws. SIAM J. Sci. Comput. 40 (2018) A288–A305. [Google Scholar]
  10. C. Cichowlas and M.E. Brachet, Evolution of complex singularities in Kida-Pelz and Taylor-Green inviscid flows. Fluid Dyn. Res. 36 (2005) 239–248. [Google Scholar]
  11. G.M. Coclite and M.M. Coclite, Conservation laws with singular nonlocal sources. J. Differ. Equ. 250 (2011) 3831–3858. [Google Scholar]
  12. G.M. Coclite and L. di Ruvo, Well-posedness of the Ostrovsky-Hunter equation under the combined effects of dissipation and short wave dispersion. J. Evol. Equ. 16 (2016) 365–389. [CrossRef] [Google Scholar]
  13. G.M. Coclite and E. Jannelli, Well-posedness for a slow erosion model. J. Math. Anal. App. 456 (2017) 337–355. [CrossRef] [Google Scholar]
  14. G.M. Coclite, H. Holden and K.H. Karlsen, Wellposedness for a parabolic-elliptic system. Discrete Contin. Dyn. Syst. 13 (2005) 659–682. [CrossRef] [Google Scholar]
  15. G.M. Coclite, K.H. Karlsen, S. Mishra and N.H. Risebro, Convergence of vanishing viscosity approximations of 2 × 2 triangular systems of multi-dimensional conservation laws. Boll. Unione Mat. Ital. 2 (2009) 275–284. [Google Scholar]
  16. G.M. Coclite, S. Mishra and N.H. Risebro, Convergence of an Engquist-Osher scheme for a multidimensional triangular system of conservation laws. Math. Comput. 79 (2010) 71–94. [Google Scholar]
  17. G.M. Coclite, F. Gargano and V. Sciacca, Analytic solutions and singularity formation for the peakon b-family equations. Acta Appl. Math. 122 (2012) 419–434. [Google Scholar]
  18. G.M. Coclite, L. di Ruvo, J. Ernest and S. Mishra, Convergence of vanishing capillarity approximations for scalar conservation laws with discontinuous fluxes. Netw. Heterogen. Media 8 (2013) 969–984. [CrossRef] [MathSciNet] [Google Scholar]
  19. S.J. Cowley, Computer extension and analytic continuation of Blasius’ expansion for impulsively flow past a circular cylinder. J. Fluid Mech. 135 (1983) 389–405. [Google Scholar]
  20. M.G. Crandall and A. Majda, Monotone difference approximations for scalar conservation laws. Math. Comput. 34 (1980) 1–21. [Google Scholar]
  21. G. Della Rocca, M.C. Lombardo, M. Sammartino and V. Sciacca, Singularity tracking for Camassa-Holm and Prandtl’s equations. Appl. Numer. Math. 56 (2006) 1108–1122. [Google Scholar]
  22. B. Engquist and S. Osher, One sided difference approximations for nonlinear conservation laws. Math. Comput. 36 (1980) 45–75. [Google Scholar]
  23. R. Eymard, T. Gallouët, M. Ghilani and R. Herbin, Error estimates for the approximate solutions of a nonlinear hyperbolic equation given by finite volume schemes. IMA J. Numer. Anal. 18 (1998) 563–594. [CrossRef] [MathSciNet] [Google Scholar]
  24. J. Friedrich, O. Kolb and S. Göttlich, A Godunov type scheme for a class of LWR traffic flow models with non-local flux. Netw. Heterogen. Media 13 (2018) 531–547. [CrossRef] [Google Scholar]
  25. U. Frisch, T. Matsumoto and J. Bec, Singularities of Euler flow? Not out of the blue!. J. Stat. Phys. 113 (2003) 761–781. [Google Scholar]
  26. F. Gargano, M. Sammartino and V. Sciacca, Singularity formation for Prandtl’s equations. Phys. D 238 (2009) 1975–1991. [CrossRef] [Google Scholar]
  27. F. Gargano, M. Sammartino, V. Sciacca and K.W. Cassel, Analysis of complex singularities in high-Reynolds-number Navier-Stokes solutions. J. Fluid Mech. 747 (2014) 381–421. [Google Scholar]
  28. F. Gargano, G. Ponetti, M. Sammartino and V. Sciacca, Complex singularities in KdV solutions. Ricerche Mat. 65 (2016) 479–490. [CrossRef] [Google Scholar]
  29. F. Gargano, M.M.L. Sammartino and V. Sciacca, Fluid mechanics: Singular behavior of a vortex layer in the zero thickness limit. Rend. Lincei Mat. Appl. 28 (2017) 553–572. [Google Scholar]
  30. E. Godlewski and P.-A. Raviart, Hyperbolic Systems of Conservation Laws. In: Mathematiques et Applications. Ellipses, Paris (1991). [Google Scholar]
  31. K.P. Hadeler and C. Kuttler, Dynamical models for granular matter. Granular Matter 2 (1999) 9–18. [Google Scholar]
  32. K.H. Karlsen and N.H. Risebro, Convergence of finite difference schemes for viscous and inviscid conservation laws with rough coefficients. M2AN 35 (2001) 239–269. [CrossRef] [EDP Sciences] [Google Scholar]
  33. C. Klein and K. Roidot, Numerical study of shock formation in the dispersionless Kadomtsev-Petviashvili equation and dispersive regularizations. Phys. D 265 (2013) 1–25. [CrossRef] [Google Scholar]
  34. R. Krasny, A study of singularity formation in a vortex sheet by the point-vortex approximation. J. Fluid Mech. 167 (1986) 65–93. [Google Scholar]
  35. D. Li and T. Li, Shock formation in a traffic flow model with Arrhenius look-ahead dynamics. Netw. Heterogen. Media 6 (2011) 681–694. [CrossRef] [Google Scholar]
  36. T. Matsumoto, J. Bec and U. Frisch, The analytic structure of 2D Euler flow at short times. Fluid Dyn. Res. 36 (2005) 221–237. [Google Scholar]
  37. F. Murat, L’injection du cône positif de H−1 dans W−1,q est compacte pour tout q < 2. J. Math. Pures Appl. 60 (1981) 309–322. [Google Scholar]
  38. W. Pauls, T. Matsumoto, U. Frisch and J. Bec, Nature of complex singularities for the 2D Euler equation. Phys. D 219 (2006) 40–59. [CrossRef] [Google Scholar]
  39. T. Rehman, G. Gambino and S.R. Choudhury, Smooth and non-smooth traveling wave solutions of some generalized camassa-holm equations. Commun. Nonlinear Sci. Numer. Simul. 19 (2014) 1746–1769. [Google Scholar]
  40. M.J. Shelley, A study of singularity formation in vortex–sheet motion by a spectrally accurate vortex method. J. Fluid. Mech. 244 (1992) 493–526. [Google Scholar]
  41. W. Shen and T. Zhang, Erosion profile by a global model for granular flow. Arch. Ration. Mech. Anal. 204 (2012) 837–879. [Google Scholar]
  42. S.-I. Sohn, Singularity formation and nonlinear evolution of a viscous vortex sheet model. Phys. Fluids 25 (2013) 014106. [CrossRef] [Google Scholar]
  43. C. Sulem, P.-L. Sulem and H. Frisch, Tracing complex singularities with spectral methods. J. Comput. Phys. 50 (1983) 138–161. [Google Scholar]
  44. L. Tartar, Compensated compactness and applications to partial differential equations. In: Vol. IV of Nonlinear Analysis and Mechanics: Heriot–Watt Symposium. Vol. 39 of Res. Notes in Math. Pitman, Boston, MA-London (1979) 136–212. [Google Scholar]

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