We investigate existence and uniqueness of solutions to the filtration equation with an inhomogeneous density in (), approaching at infinity a given continuous datum of Dirichlet type.
@article{AIHPC_2014__31_2_413_0, author = {Grillo, Gabriele and Muratori, Matteo and Punzo, Fabio}, title = {Conditions at infinity for the inhomogeneous filtration equation}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {413--428}, publisher = {Elsevier}, volume = {31}, number = {2}, year = {2014}, doi = {10.1016/j.anihpc.2013.04.002}, mrnumber = {3181677}, zbl = {1302.35193}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2013.04.002/} }
TY - JOUR AU - Grillo, Gabriele AU - Muratori, Matteo AU - Punzo, Fabio TI - Conditions at infinity for the inhomogeneous filtration equation JO - Annales de l'I.H.P. Analyse non linéaire PY - 2014 SP - 413 EP - 428 VL - 31 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2013.04.002/ DO - 10.1016/j.anihpc.2013.04.002 LA - en ID - AIHPC_2014__31_2_413_0 ER -
%0 Journal Article %A Grillo, Gabriele %A Muratori, Matteo %A Punzo, Fabio %T Conditions at infinity for the inhomogeneous filtration equation %J Annales de l'I.H.P. Analyse non linéaire %D 2014 %P 413-428 %V 31 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2013.04.002/ %R 10.1016/j.anihpc.2013.04.002 %G en %F AIHPC_2014__31_2_413_0
Grillo, Gabriele; Muratori, Matteo; Punzo, Fabio. Conditions at infinity for the inhomogeneous filtration equation. Annales de l'I.H.P. Analyse non linéaire, Volume 31 (2014) no. 2, pp. 413-428. doi : 10.1016/j.anihpc.2013.04.002. http://www.numdam.org/articles/10.1016/j.anihpc.2013.04.002/
[1] Stabilization of solutions of a degenerate nonlinear diffusion problem, Nonlinear Anal. TMA 6 (1982), 1001-1022 | MR | Zbl
, , ,[2] Continuity of weak solutions to a general porous medium equation, Indiana Univ. Math. J. 32 (1983), 83-118 | MR
,[3] A boundary modulus of continuity for a class of singular parabolic equations, J. Differential Equations 63 (1986), 418-447 | MR
,[4] -functional inequalities and weighted porous media equations, Potential Anal. 28 (2008), 35-59 | MR | Zbl
, , , ,[5] On the Bakry–Emery criterion for linear diffusions and weighted porous media equations, Commun. Math. Sci. 6 (2008), 477-494 | MR | Zbl
, , ,[6] The Cauchy problem for the nonlinear filtration equation in an inhomogeneous medium, J. Differential Equations 84 (1990), 309-318 | MR | Zbl
,[7] The filtration equation in a class of functions decreasing at infinity, Proc. Amer. Math. Soc. 120 (1994), 825-830 | MR | Zbl
, ,[8] Sharp short and long time bounds for solutions to porous media equations with Neumann boundary conditions, J. Differential Equations 254 (2013), 2261-2288 | MR | Zbl
, ,[9] Porous media equations with two weights: existence, uniqueness, smoothing and decay properties of energy solutions via Poincaré inequalities, Discrete Contin. Dyn. Syst. Ser. A 33 (2013), 3599-3640 | MR | Zbl
, , ,[10] Disappearing interfaces in nonlinear diffusion, Adv. Math. Sci. Appl. 7 (1997), 695-710 | MR | Zbl
, , ,[11] Long time behavior for the inhomogeneous PME in a medium with rapidly decaying density, Discrete Contin. Dyn. Syst. 26 (2010), 521-549 | MR | Zbl
, , ,[12] Admissible conditions for parabolic equations degenerating at infinity, St. Petersburg Math. J. 19 (2008), 239-251 | MR | Zbl
, , ,[13] Propagation of thermal waves in an inhomogeneous medium, Comm. Pure Appl. Math. 34 (1981), 831-852 | MR | Zbl
, ,[14] Non-linear diffusion in a finite mass medium, Comm. Pure Appl. Math. 35 (1982), 113-127 | MR | Zbl
, ,[15] Linear and Quasilinear Equations of Parabolic Type, Nauka, Mocow (1967), Transl. Math. Monogr. vol. 23, AMS, Providence (1968) | MR | Zbl
, , ,[16] On the Cauchy problem for nonlinear parabolic equations with variable density, J. Evol. Equ. 9 (2009), 429-447 | MR | Zbl
,[17] Uniqueness and nonuniqueness of bounded solutions to singular nonlinear parabolic equations, Nonlinear Anal. TMA 70 (2009), 3020-3029 | MR | Zbl
,[18] On support of solutions to singular nonlinear parabolic equations in bounded domains, Interfaces Free Bound. 13 (2011), 397-410 | MR | Zbl
,[19] Uniqueness and support properties of solutions to singular quasilinear parabolic equations on surfaces of revolution, Ann. Mat. Pura Appl. 191 (2012), 311-338 | MR | Zbl
,[20] Uniqueness and nonuniqueness of solutions to quasilinear parabolic equations with a singular coefficient on weighted Riemannian manifolds, Asymptot. Anal. 79 (2012), 273-301 | MR | Zbl
,[21] The Cauchy problem for the inhomogeneous porous medium equation, Netw. Heterog. Media 2 (2006), 337-351 | MR | Zbl
, ,[22] The inhomogeneous PME in several space dimensions. Existence and uniqueness of finite energy solutions, Commun. Pure Appl. Anal. 7 (2008), 1275-1294 | MR
, ,[23] Long time behavior for the inhomogeneous PME in a medium with slowly decaying density, Commun. Pure Appl. Anal. 8 (2009), 493-508 | MR | Zbl
, ,[24] The Porous Medium Equation. Mathematical Theory, The Clarendon Press, Oxford University Press, Oxford (2007) | MR
,Cited by Sources: