Free Access
Volume 25, 2019
Article Number 46
Number of page(s) 37
Published online 25 September 2019
  1. T. Barker, D.G. Schaeffer, P. Bohorquez and J.M.N.T. Gray, Well-posed and ill-posed behavior of the μ(I)-rheology for granular flow. J. Fluid Mech. 779 (2015) 794–818. [Google Scholar]
  2. G. Bellettini, V. Caselles and M. Novaga, The total variation flow in ℝN. J. Differ. Equ. 184 (2002) 475–525. [Google Scholar]
  3. F. Bouchut, R. Eymard and A. Prignet, Convergence of conforming approximations for inviscid incompressible Bingham fluid flows and related problems. J. Evol. Equ. 14 (2014) 635–669. [CrossRef] [Google Scholar]
  4. F. Bouchut, I.R. Ionescu and A. Mangeney, An analytic approach for the evolution of the static/flowing interface in viscoplastic granular flows. Commun. Math. Sci. 14 (2016) 14. [Google Scholar]
  5. O. Cazacu and I.R. Ionescu, Compressible rigid viscoplastic fluids. J. Mech. Phys. Solids 54 (2006) 1640–1667 [Google Scholar]
  6. G. Duvaut and J.-L. Lions, Inequalities in mechanics and physics. Translated from the French by C. W. John. Grundlehren der Mathematischen Wissenschaften. Springer-Verlag, Berlin, New York (1976). [CrossRef] [Google Scholar]
  7. L.C. Evans, Partial differential equations, 2nd edn. Vol. 19 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI, (2010). [CrossRef] [Google Scholar]
  8. M. Fuchs and G. Seregin, Variational methods for problems from plasticity theory and for generalized Newtonian fluids. Vol. 1749 of Lecture Notes in Mathematics. Springer-Verlag, Berlin (2000). [CrossRef] [Google Scholar]
  9. M. Giaquinta, Multiple integrals in the calculus of variations and nonlinear elliptic systems. Vol. 105 of Annals of Mathematics Studies. Princeton University Press, Princeton, NJ (1983). [Google Scholar]
  10. M.-H. Giga, Y. Giga and N. Požár, Periodic total variation flow of non-divergence type in ℝn. J. Math. Pures Appl. 102 (2014) 203–233. [Google Scholar]
  11. Y. Giga and N. Požár, A level set crystalline mean curvature flow of surfaces. Adv. Differ. Equ. 21 (2016) 631–698. [Google Scholar]
  12. I.R. Ionescu, A. Mangeney, F. Bouchut and O. Roche, Viscoplastic modeling of granular column collapse with pressure-dependent rheology. J. Non-Newton. Fluid Mech. 219 (2015) 1–18. [CrossRef] [Google Scholar]
  13. P. Jop, Y. Forterre and O. Pouliquen, A constitutive law for dense granular flows. Nature 441 (2006) 727–730. [CrossRef] [PubMed] [Google Scholar]
  14. D. Krejčiřík and A. Pratelli, The Cheeger constant of curved strips. Pac. J. Math. 254 (2011) 309–333. [CrossRef] [MathSciNet] [Google Scholar]
  15. F. Krügel, Some properties of minimizers of a variational problem involving the total variation functional. Commun. Pure Appl. Anal. 14 (2015) 341–360 [CrossRef] [Google Scholar]
  16. F. Krügel, Potential theory for the sum of the 1-Laplacian and p-Laplacian. Nonlinear Anal. 112 (2015) 165–180. [CrossRef] [Google Scholar]
  17. G.P. Leonardi and A. Pratelli, On the Cheeger sets in strips and non-convex domains. Calc. Var. Partial Differ. Equ. 55 (2016) 15. [Google Scholar]
  18. G. Leoni, A first course in Sobolev spaces. Vol. 105 of Graduate Studies in Mathematics. American Mathematical Society, Providence, RI (2009). [CrossRef] [Google Scholar]
  19. C. Lusso, F. Bouchut, A. Ern, A. Mangeney. A Free Interface Model for Static/Flowing Dynamics in Thin-Layer Flows of Granular Materials with Yield: Simple Shear Simulations and Comparison with Experiments. Appl. Sci. 7 (2017) 386. [CrossRef] [Google Scholar]
  20. C. Lusso, A. Ern, F. Bouchut, A. Mangeney, M. Farin and O. Roche. Two-dimensional simulation by regularization of free surface viscoplastic flows with Drucker–Prager yield stress and application to granular collapse. J. Comput. Phys. 333 (2017) 387–408. [Google Scholar]
  21. J. Málek, J. Nečas, M. Rokyta and M. Ružička. Weak and measure-valued solutions to evolutionary PDEs. Vol. 13 of Applied Mathematics and Mathematical Computation. Chapman & Hall, London (1996). [Google Scholar]
  22. O. Pouliquen, C. Cassar, P. Jop, Y. Forterre and M. Nicolas. Flow of dense granular material: towards simple constitutive laws. J. Stat. Mech.: Theo. Exp. 7 (2006) P07020. [Google Scholar]
  23. G. Seregin, Continuity for the strain velocity tensor in two-dimensional variational problems from the theory of the Bingham fluid. Ital. J. Pure Appl. Math. 2 (1998) 141–150. [Google Scholar]
  24. D.G Schaeffer, Instability in the evolution equations describing incompressible granular flow. J. Differ. Equ. 66 (1987) 19–50. [Google Scholar]
  25. F.A. Vaillo, V. Caselles and J. M. Mazón, Parabolic Quasilinear Equations Minimizing Linear Growth Functionals. Vol. 223 of Progress in Mathematics. Birkhäuser Verlag, Basel (2004). [Google Scholar]
  26. W.P. Ziemer, Weakly Differentiable Functions. Vol. 120 of Graduate Texts in Mathematics. Springer-Verlag, New York (1989). [CrossRef] [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.