References
- Bénilan Ph, Crandall MG, Pierre M. Solutions of the porous medium equation in ℝN under optimal conditions on initial values. Indiana Univ Math J. 1984;33:51–87.
- Zhang QS. Blow-up results for nonlinear parabolic equations on manifolds. Duke Math J. 1999;97:515–539.
- Punzo F. On well-posedness of semilinear parabolic and elliptic problems in the hyperbolic space. J. Differ Equ. 2011;251:1972–1989.
- Punzo F. Support properties of solutions to nonlinear parabolic equations with variable density in the hyperbolic space. Discrete Contin Dyn Syst S. 2012;5:657–670.
- Punzo F. Uniqueness and support properties of solutions to singular quasilinear parabolic equations on surfaces of revolution. Ann Mat Pura Appl. 2012;191:311–338.
- Punzo F. Well-posedness of the Cauchy problem for nonlinear parabolic equations with variable density in the hyperbolic space. NoDEA Nonlinear Differ Equ Appl. 2012;19:485–501.
- Grillo G, Muratori M. Radial fast diffusion on the hyperbolic space. Proc Lond Math Soc. 2014;109:283–317.
- Matano H, Punzo F, Tesei A. Front propagation for nonlinear diffusion equations on the hyperbolic space. J Eur Math Soc (JEMS). 2015;17:1199–1227.
- Vázquez JL. Fundamental solution and long time behavior of the porous medium equation in hyperbolic space. J Math Pures Appl. 2015;104:454–484.
- Grillo G, Muratori M. Smoothing effects for the porous medium equation on Cartan--Hadamard manifolds. Nonlinear Anal. 2016;131:346–362.
- Grillo G, Muratori M, Vázquez JL. The porous medium equation on Riemannian manifolds with negative curvature The large-time behaviour. Adv Math. 2017;314:328–377.
- Mastrolia P, Monticelli DD, Punzo F. Nonexistence of solutions to parabolic differential inequalities with a potential on Riemannian manifolds. Math Ann. 2017;367:929–963.
- Grillo G, Muratori M, Punzo F. The porous medium equation with large initial data on negatively curved Riemannian manifolds. J Math Pures Appl. Forthcoming. DOI:10.1016/j.matpur.2017.07.021
- Grillo G, Muratori M, Punzo F. The porous medium equation with measure data on negatively curved Riemannian manifolds. accepted on J Eur Math Soc (JEMS). Preprint arXiv: http://arxiv.org/pdf/1507.08883
- Punzo F. Uniqueness and non-uniqueness of solutions to quasilinear parabolic equations with a singular coefficient on weighted Riemannian manifolds. Asymptot Anal. 2012;79:273–301.
- Murata M. Nonuniqueness of the positive Dirichlet problem for parabolic equations in cylinders. J Funct Anal. 1996;135:456–487.
- Ishige K. An intrinsic metric approach to uniqueness of the positive Dirichlet problem for parabolic equations in cylinders. J Differ Equ. 1999;158:251–290.
- Ishige K, Murata M. Uniqueness of nonnegative solutions of the Cauchy problem for parabolic equations on manifolds or domains. Ann Scuola Norm Sup Pisa Cl Sci. 2001;30:171–223.
- Ishige K. An intrinsic metric approach to uniqueness of the positive Cauchy-Neumann problem for parabolic equations. J Math Anal Appl. 2002;276:763–790.
- Murata M. Heat escape. Math Ann. 2003;327:203–226.
- Vázquez JL. The Porous medium equation mathematical theory. Oxford mathematical monographs. Oxford: The Clarendon Press, Oxford University Press; 2007.
- Muskat M. The flow of homogeneous fluids through porous media. New York (NY): McGraw-Hill Book Company; 1937.
- Grigor’yan A. Analytic and geometric background of recurrence and non-explosion of the Brownian motion on Riemannian manifolds. Bull Amer Math Soc. 1999;36:135–249.
- Grigor’yan A. Heat Kernel and analysis on manifolds, AMS/IP studies in advanced mathematics. Vol. 47. Providence (RI): American Mathematical Society; 2009.
- Aronson DG, Crandall MG, Peletier LA. Stabilization of a degenerate nonlinear diffusion problem. Nonlinear Anal. 1982;6:1001–1022.
- Pierre M. Uniqueness of the solutions of ut-Δφ(u) with initial datum a measure. Nonlinear Anal. 1982;6:175–187.