On Fourier series in eigenfunctions of elliptic boundary value problems, Georgian Math. J, vol.10, issue.3, p.401410, 2003. ,
Porous medium ow with both a fractional potential pressure and fractional time derivative, Chin. Ann. Math. Ser. B, vol.38, issue.1, p.4582, 2017. ,
Singularity formation in Hele-Shaw bubbles, Phys. Fluids, vol.8, issue.2, pp.344-352, 1996. ,
The porous medium equation, Nonlinear diusion problems, vol.1224, p.146, 1985. ,
A bound from below on the temperature for the NavierStokes-Fourier system, SIAM J. Math. Anal, vol.45, issue.4, p.20462063, 2013. ,
Dynamics of uids in porous media, vol.27, 1972. ,
Nonnegative solutions of a fourth-order nonlinear degenerate parabolic equation, Arch. Rational Mech. Anal, vol.129, issue.2, p.175200, 1995. ,
Source type solutions of a fourth order nonlinear degenerate parabolic equation, Nonlinear Anal, vol.18, issue.3, p.217234, 1992. ,
Finite speed of propagation and continuity of the interface for thin viscous ows, Adv. Dierential Equations, vol.1, issue.3, p.337368, 1996. ,
Higher order nonlinear degenerate parabolic equations, J. Dierential Equations, vol.83, issue.1, p.179206, 1990. ,
The lubrication approximation for thin viscous lms: the moving contact line with a porous media cut-o of van der Waals interactions, Nonlinearity, vol.7, issue.6, p.15351564, 1994. ,
The lubrication approximation for thin viscous lms: regularity and long-time behavior of weak solutions ,
, Comm. Pure Appl. Math, vol.49, issue.2, p.85123, 1996.
The mathematics of moving contact lines in thin liquid lms, Notices Amer. Math. Soc, vol.45, issue.6, p.689697, 1998. ,
Singularities and similarities in interface ows, Trends and perspectives in applied mathematics, vol.100, p.155208, 1994. ,
Barenblatt proles for a nonlocal porous medium equation, C. R. Math. Acad. Sci, vol.349, p.641645, 2011. ,
The nonlocal porous medium equation: Barenblatt proles and other weak solutions, Arch. Ration. Mech. Anal, vol.215, issue.2, pp.497-529, 2015. ,
Recherches théoriques sur l'écoulement des nappes d'eau inltrées dans le sol et sur le débit des sources, Journal de mathématiques pures et appliquées, vol.10, pp.5-78, 1904. ,
Regularity theory for parabolic nonlinear integral operators, J. Amer. Math. Soc, vol.24, issue.3, p.849869, 2011. ,
Regularity of solutions of the fractional porous medium ow, J. Eur. Math. Soc, vol.15, issue.5, p.17011746, 2013. ,
The De Giorgi method for regularity of solutions of elliptic equations and its applications to uid dynamics, Discrete Contin. Dyn. Syst. Ser. S, vol.3, issue.3, p.409427, 2010. ,
Nonlinear porous medium ow with fractional potential pressure, Arch. Ration. Mech. Anal, vol.202, issue.2, p.537565, 2011. ,
Regularity of solutions of the fractional porous medium ow with exponent 1/2. Algebra i Analiz, St. Petersburg Mathematical Journal, vol.27, issue.3, 2015. ,
The De Giorgi method for regularity of solutions of elliptic equations and its applications to uid dynamics ,
, Dyn. Syst. Ser. S, vol.3, issue.3, p.409427, 2010.
Asymptotic behaviour of a porous medium equation with fractional diusion, Discrete Contin. Dyn. Syst, vol.29, issue.4, p.13931404, 2011. ,
Global regularity of solutions to systems of reaction-diusion with sub-quadratic growth in any dimension, Comm. Partial Dierential Equations, vol.34, p.12281250, 2009. ,
Long-time asymptotics for strong solutions of the thin lm equation, Comm. Math. Phys, vol.225, issue.3, p.551571, 2002. ,
On a fourth-order degenerate parabolic equation: global entropy estimates, existence, and qualitative behavior of solutions, SIAM J. Math. Anal, vol.29, issue.2, p.321342, 1998. ,
Waiting time phenomena for degenerate parabolic equationsa unifying approach, Geometric analysis and nonlinear partial dierential equations, p.637648, 2003. ,
Sulla dierenziabilità e l'analiticità delle estremali degli integrali multipli regolari, Mem. Accad. Sci. Torino. Cl. Sci. Fis. Mat. Nat, vol.3, issue.3, p.2543, 1957. ,
A fractional porous medium equation, Advances in Mathematics, vol.226, issue.2, pp.1378-1409, 2011. ,
A general fractional porous medium equation, Communications on Pure and Applied Mathematics, vol.65, issue.9, p.12421284, 2012. ,
On the local behaviour of solutions of degenerate parabolic equations with measurable coecients, Ann. Scuola Norm. Sup. Pisa Cl. Sci, vol.13, issue.4, p.487535, 1986. ,
Harnack type estimates and Hölder continuity for non-negative solutions to certain sub-critically singular parabolic partial dierential equations, Manuscripta Math, vol.131, issue.1-2, p.231245, 2010. ,
Harnack inequalities for quasiminima of variational integrals, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.1, issue.4, p.295308, 1984. ,
Forward, backward and elliptic Harnack inequalities for non-negative solutions to certain singular parabolic partial dierential equations, Ann. Sc. Norm. Super. Pisa Cl. Sci, vol.9, issue.5, p.385422, 2010. ,
Harnack's inequality for degenerate and singular parabolic equations, 2012. ,
On the Cahn-Hilliard equation with degenerate mobility, SIAM J. Math. Anal, vol.27, issue.2, p.404423, 1996. ,
Local regularity for parabolic nonlocal operators, Comm. Partial Dierential Equations, vol.38, issue.9, p.15391573, 2013. ,
A rapid method of predicting width and extent of hydraulically induced fractures, J. Pet. Technol, vol.21, p.157181, 1969. ,
Elliptic partial dierential equations of second order, Classics in Mathematics, 2001. ,
Clément Mouhot, and Alexis Vasseur. Harnack inequality for kinetic fokker-planck equations with rough coecients and application to the landau equation, 2017. ,
Regularity analysis for systems of reactiondiusion equations, Ann. Sci. Éc. Norm. Supér, vol.43, issue.4, p.117142, 2010. ,
On the motion of a small viscous droplet that wets a surface, J. Fluid Mech, 1978. ,
On the wetting of a surface by a very viscous uid, Stud. Appl. Math, 1981. ,
Degenerate parabolic dierential equations of fourth order and a plasticity model with non-local hardening, Z. Anal. Anwendungen, vol.14, issue.3, p.541574, 1995. ,
On Bernis' interpolation inequalities in multiple space dimensions, Z. Anal. Anwendungen, vol.20, issue.4, p.987998, 2001. ,
Droplet spreading under weak slippage: the optimal asymptotic propagation rate in the multi-dimensional case, Interfaces Free Bound, vol.4, issue.3, p.309323, 2002. ,
Droplet spreading under weak slippage: a basic result on nite speed of propagation, SIAM J. Math. Anal, vol.34, issue.4, p.9921006, 2003. ,
Sliding and spreading of thin two-dimensional drops, Quart. J. Mech. Appl. Math, 1981. ,
Some aspects of the thin lm equation, European Congress of Mathematics, vol.II, p.291301, 2000. ,
Self-similar solutions for a fractional thin lm equation governing hydraulic fractures ,
Self-similar solutions for a fractional thin lm equation governing hydraulic fractures, Communications in Mathematical Physics, vol.340, issue.3, pp.1187-1229, 2015. ,
Finite speed of propagation for a non-local porous medium equation, Colloq. Math, vol.143, issue.2, p.149157, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01081958
Existence of solutions for a higher order non-local equation appearing in crack dynamics, Nonlinearity, vol.24, issue.12, p.34873514, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00451017
Weak harnack inequality for the boltzmann equation without cut-o, 2016. ,
A priori estimates for integro-dierential operators with measurable kernels, Calc. Var. Partial Dierential Equations, vol.34, issue.1, p.121, 2009. ,
A property of the solutions of parabolic equations with measurable coecients, Izv. Akad. Nauk SSSR Ser. Mat, vol.44, issue.1, p.239, 1980. ,
The motion with slip of a thin viscous droplet over a solid surface, Stud. Appl. Math, vol.67, issue.3, p.217230, 1982. ,
Ural'tceva. Linear and quasilinear equations of parabolic type, Translated from the Russian by S. Smith. Translations of Mathematical Monographs, vol.23, 1968. ,
Ural'tseva. Linear and quasilinear elliptic equations. Translated from the Russian by Scripta Technica, Inc. Translation editor: Leon Ehrenpreis, 1968. ,
Ural'tseva. Linear and quasilinear elliptic equations. Translated from the Russian by Scripta Technica, Inc. Translation editor: Leon Ehrenpreis, 1968. ,
The motion of a gas in a porous medium, Complete Works, Acad. Sciences URSS, 1930. ,
Second order parabolic dierential equations. World scientic, 1996. ,
Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, 1969. ,
A new proof of De Giorgi's theorem concerning the regularity problem for elliptic dierential equations, Comm. Pure Appl. Math, vol.13, p.457468, 1960. ,
The ow of homogeneous uids through porous media, 1937. ,
Continuity of solutions of parabolic and elliptic equations, Amer. J. Math, vol.80, p.931954, 1958. ,
Applied partial dierential equations, 2003. ,
A dual mesh multigrid preconditioner for the ecient solution of hydraulically driven fracture problems, Internat. J. Numer. Methods Engrg, vol.63, issue.13, p.17971823, 2005. ,
An Eulerian moving front algorithm with weak-form tip asymptotics for modeling hydraulically driven fractures, Comm. Numer. Methods Engrg, vol.25, issue.2, p.185200, 2009. ,
Theory of ground water movement, 1962. ,
Self-similar solutions for elastohydrodynamic cavity ow, Proc. Roy. Soc. London Ser. A, vol.400, p.289313, 1819. ,
Finite and innite speed of propagation for porous medium equations with nonlocal pressure, J. Dierential Equations, vol.260, issue.2, p.11541199, 2016. ,
Study of a family of higher order nonlocal degenerate parabolic equations: from the porous medium equation to the thin lm equation, J. Dierential Equations, vol.259, issue.11, p.57825812, 2015. ,
Higher derivatives estimate for the 3D Navier-Stokes equation, Ann. Inst. H. Poincaré Anal. Non Linéaire, vol.27, issue.5, p.11891204, 2010. ,
The De Giorgi method for elliptic and parabolic equations and some applications, Lectures on the analysis of nonlinear partial dierential equations. Part, vol.4, p.195222, 2016. ,
The porous medium equation, Oxford Mathematical Monographs. The Clarendon Press, 2007. ,
Harnack inequalities for functions in De Giorgi parabolic class, Partial dierential equations, vol.1306, p.182201, 1986. ,
Harnack inequalities for functions in the general De Giorgi parabolic class, Chinese Ann. Math. Ser. B, vol.10, issue.2, p.387, 1989. ,
Physics of shock waves and high-temperature hydrodynamic phenomena, 1966. ,
On hydraulic fracturing of an oil-bearing stratum, Izv. Akad. Nauk. SSSR. Otdel Tekhn. Nauk, vol.5, p.341, 1955. ,