Entropy formulation for fractal conservation laws, J. Evol. Equ, vol.7, issue.1, pp.145-175, 2007. ,
URL : https://hal.archives-ouvertes.fr/hal-00474312
Non-uniqueness of weak solutions for fractal Burgers equation, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.27, issue.4, pp.997-1016, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00405892
Nonlocal dissipation measure and L 1 kinetic theory for fractional conservation laws, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02320423
Optimal continuous dependence estimates for fractional degenerate parabolic equations, Arch. Ration. Mech. Anal, vol.213, issue.3, pp.705-762, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-00841159
Occurrence and non-appearance of shocks in fractal Burgers equations, J. Hyperbolic Differ. Equ, vol.4, issue.3, pp.479-499, 2007. ,
Optimal and dual stability results for L 1 viscosity and L ? entropy solutions ,
URL : https://hal.archives-ouvertes.fr/hal-01945687
Existence of renormalized solutions of degenerate elliptic-parabolic problems, Proc. Roy. Soc. Edinburgh Sect. A, vol.133, issue.3, pp.477-496, 2003. ,
L 1 theory of scalar conservation law with continuous flux function, J. Funct. Anal, vol.171, issue.1, pp.15-33, 2000. ,
A note on uniqueness of entropy solutions to degenerate parabolic equations in R N, NoDEA Nonlinear Differ. Eq. Appl, vol.17, issue.1, pp.109-118, 2010. ,
URL : https://hal.archives-ouvertes.fr/hal-00378475
On classes of well-posedness for quasilinear diffusion equations in the whole space, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02328003
A note on entropy solutions for degenerate parabolic equations with L 1 ? L p data, Int. J. Dyn. Syst. Differ. Equ, vol.4, issue.1-2, pp.78-92, 2012. ,
Équations d'évolution dans un espace de Banach quelconque et applications, 1972. ,
Solutions of the porous medium equation in RN under optimal conditions on initial values, Indiana Univ. Math. J, vol.33, issue.1, pp.51-87, 1984. ,
Quantitative local and global a priori estimates for fractional nonlinear diffusion equations, Adv. Math, vol.250, pp.242-284, 2014. ,
A priori estimates for fractional nonlinear degenerate diffusion equations on bounded domains, Arch. Ration. Mech. Anal, vol.218, issue.1, pp.317-362, 2015. ,
Conservation laws with continuous flux functions, NoDEA V, vol.3, pp.395-419, 1996. ,
Non-critical fractional conservation laws in domains with boundary, Netw. Heterog. Media, vol.11, issue.2, pp.251-262, 2016. ,
Uniqueness of solutions of the initial-value problem for u t ? ??(u) = 0, J. Math. Pures Appl, issue.9, pp.153-163, 1979. ,
Entropy solutions for nonlinear degenerate problems, Arch. Rational Mech. Anal, vol.147, pp.269-361, 1999. ,
Entropy solution theory for fractional degenerate convection-diffusion equations, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.28, issue.3, pp.413-441, 2011. ,
Nonlinear maximum principles for dissipative linear non-local operators and applications, Geom. Funct. Anal, vol.22, issue.5, pp.1289-1321, 2012. ,
Nonnegative solutions of the porous medium equation, Comm. Partial Differential Equations, vol.9, issue.5, pp.409-437, 1984. ,
Degenerate diffusions. Initial value problems and local regularity theory, EMS Tracts in Mathematics, 2007. ,
Uniqueness and properties of distributional solutions of non-local equations of porous medium type, Adv. Math, vol.305, pp.78-143, 2017. ,
On distributional solutions of local and non-local problems of porous medium type, C. R. Math. Acad. Sci. Paris, vol.355, issue.11, pp.1154-1160, 2017. ,
Global solution and smoothing effect for a non-local regularization of a hyperbolic equation, J. Evol. Equ, vol.3, issue.3, pp.499-521, 2003. ,
URL : https://hal.archives-ouvertes.fr/hal-00003438
L 1 Contraction for Bounded (Nonintegrable) Solutions of Degenerate Parabolic Equations, SIAM J. Math. Anal, vol.46, issue.6, pp.3957-3982, 2014. ,
Uniqueness of very weak solutions for a fractional filtration equation, 2019. ,
The Cauchy problem for u t = ?u m when 0 < m < 1, Trans. Am. Math. Soc, vol.291, issue.1, pp.145-158, 1985. ,
Front Tracking for Hyperbolic Conservation Laws, Appl. Math. Sci, vol.152, 2007. ,
Stability of entropy solutions for Lévy mixed hyperbolic parabolic equations. Electron, J. Differ. Equ, issue.116, pp.1-23, 2011. ,
Generalized solutions of the Cauchy problem in the large for first-order nonlinear equations, Dokl.Akad.Nauk URSS V, vol.187, issue.1, pp.29-32, 1969. ,
, Soviet Math.Dokl. V, vol.10, 1969.
Conservation laws with the infinite domain of dependence on initial data, Differential equations and control theory, vol.250, pp.149-162, 1991. ,
Effect of infinite speed of propagation in the non-local theory of conservation laws, Int. Conf. Differ. Equ, pp.122-136, 1995. ,
The Cauchy problem for first order quasilinear equations in the case when the domain of dependence on the initial data is infinite. (Russian). Collection of articles dedicated to the memory of I.G. Petrovskii. Vestnik Moskov, Univ. Ser. I Mat. Meh., V, vol.29, issue.1, pp.93-100, 1974. ,
First-order quasilinear conservation laws with infinite initial data dependence area, Dokl.Akad.Nauk URSS V, vol.314, issue.1, pp.79-84, 1990. ,
, Soviet Math.Dokl. V, vol.42, issue.2, pp.316-321, 1991.
Osgood's type conditions for uniqueness of entropy solutions to Cauchy problem for quasilinear conservation laws of the first order, Ann. Univ. Ferrara, V, vol.15, pp.31-53, 1994. ,
Renormalized solution for a nonlinear anisotropic degenerated parabolic equation with nonlipschitz convection and diffusion flux functions, Int. J. of Evol. Eq, issue.4, 2008. ,
Uniqueness of entropy solutions for nonlinear degenerate parabolic problem, J. Evol. Equ. V, vol.3, issue.4, pp.603-622, 2003. ,
Direct methods in the theory of elliptic equations, 2012. ,
Explicit conditions for the uniqueness of solutions for parabolic degenerate problems, Int. J. Dyn. Syst. Differ. Equ, vol.6, issue.1, pp.75-86, 2015. ,
Uniqueness of entropy solution for general anisotropic convection-diffusion problems, Port. Math, vol.69, issue.2, pp.141-158, 2012. ,
Uniqueness of the solutions of u t ? ??(u) = 0 with initial datum a measure, Nonlinear Anal, vol.6, issue.2, pp.175-187, 1982. ,
Théorie des distributions, 1966. ,
An existence result for scalar conservation laws using measure valued solutions, Comm. Partial Differ. Equ, vol.14, issue.10, pp.1329-1350, 1989. ,
An introduction to Sobolev spaces and interpolation spaces, Lect. Notes Unione Mat. Italiana, vol.3, 2007. ,
The porous medium equation. Mathematical theory, Oxford Mathematical Monographs, 2007. ,