Open Access
Issue
ESAIM: M2AN
Volume 58, Number 4, July-August 2024
Page(s) 1301 - 1315
DOI https://doi.org/10.1051/m2an/2024043
Published online 30 July 2024
  1. S. Abe and S. Thurner, Anomalous diffusion in view of Einstein’s 1905 theory of Brownian motion. Phys. A: Stat. Mech. App. 356 (2005) 403–407. [CrossRef] [Google Scholar]
  2. N. Alibaud, Entropy formulation for fractal conservation laws. J. Evol. Equ. 7 (2007) 145–175. [CrossRef] [MathSciNet] [Google Scholar]
  3. N. Alibaud, J. Droniou and J. Vovelle, Occurrence and non-appearance of shocks in fractal Burgers equations. J. Hyperbolic Differ. Equ. 4 (2007) 479–499. [CrossRef] [Google Scholar]
  4. J.P. Bouchaud, More Lévy distributions in physics, in Lévy Flights and Related Topics in Physics. Springer Berlin Heidelberg, Berlin, Heidelberg (1995). [Google Scholar]
  5. S. Cifani and E.R. Jakobsen, On numerical methods and error estimates for degenerate fractional convection-diffusion equations. Numer. Math. 127 (2014) 447–483. [Google Scholar]
  6. S. Cifani, E.R. Jakobsen and K.H. Karlsen, The discontinuous Galerkin method for fractal conservation laws. IMA J. Numer. Anal. 31 (2011) 1090–1122. [CrossRef] [MathSciNet] [Google Scholar]
  7. R. Cont and P. Tankov, Financial Modelling with Jump Processes. Chapman & Hall/CRC Financial Mathematics Series. Chapman & Hall/CRC, Boca Raton, FL (2004). [Google Scholar]
  8. E. Di Nezza, G. Palatucci and E. Valdinoci, Hitchhiker’s guide to the fractional Sobolev spaces. Bull. Sci. Math. 136 (2012) 521–573. [Google Scholar]
  9. J. Droniou, A numerical method for fractal conservation laws. Math. Comput. 79 (2010) 95–124. [Google Scholar]
  10. J. Droniou and C. Imbert, Fractal first-order partial differential equations. Arch. Ration. Mech. Anal. 182 (2006) 299–331. [CrossRef] [MathSciNet] [Google Scholar]
  11. J. Droniou, T. Gallouet and J. Vovelle, Global solution and smoothing effect for a non-local regularization of a hyperbolic equation, in Nonlinear Evolution Equations and Related Topics: Dedicated to Philippe Bénilan. Vol. 3. Birkh¨auser Basel, Basel (2003) 499–521. [Google Scholar]
  12. B. Jourdain, S. Méléard and W.A. Woyczynski, Probabilistic approximation and inviscid limits for one-dimensional fractional conservation laws. Bernoulli 11 (2005) 689–714. [CrossRef] [MathSciNet] [Google Scholar]
  13. M.F. Shlesinger, G.M. Zaslavsky and U. Frisch, editors. Lévy Flights and Related Topics in Physics. Vol. 450 of Lecture Notes in Physics. Springer-Verlag, Berlin (1995). [CrossRef] [Google Scholar]
  14. M. Simon and C. Olivera, Non-local conservation law from stochastic particle systems. J. Dyn. Differ. Equ. 30 (2018) 1661–1682. [CrossRef] [MathSciNet] [Google Scholar]
  15. Q. Xu and J.S. Hesthaven, Discontinuous Galerkin method for fractional convection-diffusion equations. SIAM J. Numer. Anal. 52 (2014) 405–423. [CrossRef] [MathSciNet] [Google Scholar]
  16. Q. Zhang and C.-W. Shu, Error estimates to smooth solutions of Runge–Kutta discontinuous Galerkin methods for scalar conservation laws. SIAM J. Numer. Anal. 42 (2004) 641–666. [Google Scholar]
  17. Q. Zhang and C.-W. Shu, Stability analysis and a priori error estimates of the third order explicit Runge–Kutta discontinuous Galerkin method for scalar conservation laws. SIAM J. Numer. Anal. 48 (2010) 1038–1063. [CrossRef] [MathSciNet] [Google Scholar]

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