@article{AIHPC_2003__20_1_13_0,
author = {Gil, O. and Quir\'os, F.},
title = {Boundary layer formation in the transition from the porous media equation to a {Hele-Shaw} flow},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {13--36},
year = {2003},
publisher = {Elsevier},
volume = {20},
number = {1},
zbl = {1030.35107},
language = {en},
url = {https://www.numdam.org/item/AIHPC_2003__20_1_13_0/}
}
TY - JOUR AU - Gil, O. AU - Quirós, F. TI - Boundary layer formation in the transition from the porous media equation to a Hele-Shaw flow JO - Annales de l'I.H.P. Analyse non linéaire PY - 2003 SP - 13 EP - 36 VL - 20 IS - 1 PB - Elsevier UR - https://www.numdam.org/item/AIHPC_2003__20_1_13_0/ LA - en ID - AIHPC_2003__20_1_13_0 ER -
%0 Journal Article %A Gil, O. %A Quirós, F. %T Boundary layer formation in the transition from the porous media equation to a Hele-Shaw flow %J Annales de l'I.H.P. Analyse non linéaire %D 2003 %P 13-36 %V 20 %N 1 %I Elsevier %U https://www.numdam.org/item/AIHPC_2003__20_1_13_0/ %G en %F AIHPC_2003__20_1_13_0
Gil, O.; Quirós, F. Boundary layer formation in the transition from the porous media equation to a Hele-Shaw flow. Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) no. 1, pp. 13-36. https://www.numdam.org/item/AIHPC_2003__20_1_13_0/
[1] , , , Limit behaviour of focusing solutions to nonlinear diffusions, Comm. Partial Differential Equations 23 (1-2) (1998) 307-332. | Zbl | MR
[2] , , , On the limit of solutions of ut=Δum as m→∞, Rend. Sem. Mat. Univ. Politec. Torino, Fascicolo Speciale (1989) 1-13.
[3] , , The continuous dependence on ϕ of solutions of ut−Δϕ(u)=0, Indiana Univ. Math. J. 30 (1981) 161-177. | Zbl
[4] , , , Some L1 existence and dependence results for semilinear elliptic equations under nonlinear boundary conditions, Appl. Math. Optim. 17 (3) (1988) 203-224. | Zbl | MR
[5] , , Singular limit of perturbed nonlinear semigroups, Comm. Appl. Nonlinear Anal. 3 (4) (1996) 23-42. | Zbl | MR
[6] , , La limite de la solution de ut=Δpum lorsque m→∞, C. R. Acad. Sci. Paris Sér. I Math. 321 (1995) 1323-1328. | Zbl
[7] , , Continuity of the density of a gas flow in a porous medium, Trans. Amer. Math. Soc. 252 (1979) 99-113. | Zbl | MR
[8] , , Asymptotic behaviour of solutions of ut=Δum as m→∞, Indiana Univ. Math. J. 36 (4) (1987) 711-718. | Zbl
[9] , On the weak solution of moving boundary problems, J. Inst. Math. Appl. 24 (1979) 43-57. | Zbl | MR
[10] , , The ill-posed Hele-Shaw model and the Stefan problem for supercooled water, Trans. Amer. Math. Soc. 282 (1) (1984) 183-204. | Zbl | MR
[11] , , , , The mesa problem: diffusion patterns for ut=∇(um∇u) as m→∞, IMA J. Appl. Math. 37 (1986) 147-154. | Zbl
[12] , , A variational inequality approach to Hele-Shaw flow with a moving boundary, Proc. Roy. Soc. Edinburgh Sect. A 88 (1981) 93-107. | Zbl | MR
[13] , , On the mesa problem, J. Math. Anal. Appl. 123 (2) (1987) 564-571. | Zbl | MR
[14] , , Asymptotic behavior of solutions of ut=Δφm(u) as m→∞ with inconsistent initial values, in: Analyse Mathématique et applications, Gauthier-Villars, Paris, 1988, pp. 165-180. | Zbl
[15] , , Convergence of the porous media equation to Hele-Shaw, Nonlinear Anal. 44 (2001) 1111-1131. | Zbl | MR
[16] O. Gil, F. Quirós, J.L. Vázquez, Zero specific heat limit and large time asymptotics for the one-phase Stefan problem, Preprint, 2002.
[17] , The mesa-limit of the porous medium equation and the Hele-Shaw problem, Differential Integral Equations 15 (2) (2002) 129-146. | Zbl | MR
[18] , Schrödinger operators with singular potentials, Israel J. Math. 13 (1972) 133-148. | Zbl | MR
[19] , , Remarks on the quasi-steady one phase Stefan problem, Proc. Roy. Soc. Edinburgh Sect. A 102 (1986) 263-275. | Zbl | MR
[20] , , Obstructions to existence in fast-diffusion equations, J. Differential Equations 184 (2002) 348-385. | Zbl | MR
[21] , A singular limit problem for the porous medium equation, J. Math. Anal. Appl. 140 (2) (1989) 456-466. | Zbl | MR
[22] , , The penetration of fluid into a porous medium Hele-Shaw cell, Proc. Roy. Soc. A 245 (1958) 312-329. | Zbl | MR
[23] J.L. Vázquez, A new look at the zero specific heat limit of the Stefan problem, Preprint, 1998.





