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, Volume 20 (2003) no. 1, pp. 13-36.
@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},
     publisher = {Elsevier},
     volume = {20},
     number = {1},
     year = {2003},
     zbl = {1030.35107},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_2003__20_1_13_0/}
}
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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, Volume 20 (2003) no. 1, pp. 13-36. http://archive.numdam.org/item/AIHPC_2003__20_1_13_0/

[1] Aronson D.G., Gil O., Vázquez J.L., Limit behaviour of focusing solutions to nonlinear diffusions, Comm. Partial Differential Equations 23 (1-2) (1998) 307-332. | MR | Zbl

[2] Bénilan Ph., Boccardo L., Herrero M.A., On the limit of solutions of utum as m→∞, Rend. Sem. Mat. Univ. Politec. Torino, Fascicolo Speciale (1989) 1-13.

[3] Bénilan Ph., Crandall M.G., The continuous dependence on ϕ of solutions of ut−Δϕ(u)=0, Indiana Univ. Math. J. 30 (1981) 161-177. | Zbl

[4] Bénilan Ph., Crandall M.G., Sacks P., Some L1 existence and dependence results for semilinear elliptic equations under nonlinear boundary conditions, Appl. Math. Optim. 17 (3) (1988) 203-224. | MR | Zbl

[5] Bénilan Ph., Igbida N., Singular limit of perturbed nonlinear semigroups, Comm. Appl. Nonlinear Anal. 3 (4) (1996) 23-42. | MR | Zbl

[6] Bénilan Ph., Igbida N., La limite de la solution de utpum lorsque m→∞, C. R. Acad. Sci. Paris Sér. I Math. 321 (1995) 1323-1328. | Zbl

[7] Caffarelli L.A., Friedman A., Continuity of the density of a gas flow in a porous medium, Trans. Amer. Math. Soc. 252 (1979) 99-113. | MR | Zbl

[8] Caffarelli L.A., Friedman A., Asymptotic behaviour of solutions of utum as m→∞, Indiana Univ. Math. J. 36 (4) (1987) 711-718. | Zbl

[9] Crowley A.B., On the weak solution of moving boundary problems, J. Inst. Math. Appl. 24 (1979) 43-57. | MR | Zbl

[10] Di Benedetto E., Friedman A., The ill-posed Hele-Shaw model and the Stefan problem for supercooled water, Trans. Amer. Math. Soc. 282 (1) (1984) 183-204. | MR | Zbl

[11] Elliot C.M., Herrero M.A., King J.R., Ockendon J.R., The mesa problem: diffusion patterns for ut=∇(umu) as m→∞, IMA J. Appl. Math. 37 (1986) 147-154. | Zbl

[12] Elliot C.M., Janovský V., A variational inequality approach to Hele-Shaw flow with a moving boundary, Proc. Roy. Soc. Edinburgh Sect. A 88 (1981) 93-107. | MR | Zbl

[13] Friedman A., Höllig K., On the mesa problem, J. Math. Anal. Appl. 123 (2) (1987) 564-571. | MR | Zbl

[14] Friedman A., Huang S.Y., Asymptotic behavior of solutions of utφm(u) as m→∞ with inconsistent initial values, in: Analyse Mathématique et applications, Gauthier-Villars, Paris, 1988, pp. 165-180. | Zbl

[15] Gil O., Quirós F., Convergence of the porous media equation to Hele-Shaw, Nonlinear Anal. 44 (2001) 1111-1131. | MR | Zbl

[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] Igbida N., The mesa-limit of the porous medium equation and the Hele-Shaw problem, Differential Integral Equations 15 (2) (2002) 129-146. | MR | Zbl

[18] Kato T., Schrödinger operators with singular potentials, Israel J. Math. 13 (1972) 133-148. | MR | Zbl

[19] Louro B., Rodrigues J.F., Remarks on the quasi-steady one phase Stefan problem, Proc. Roy. Soc. Edinburgh Sect. A 102 (1986) 263-275. | MR | Zbl

[20] Rodriguez A., Vázquez J.L., Obstructions to existence in fast-diffusion equations, J. Differential Equations 184 (2002) 348-385. | MR | Zbl

[21] Sacks P.E., A singular limit problem for the porous medium equation, J. Math. Anal. Appl. 140 (2) (1989) 456-466. | MR | Zbl

[22] Saffman P.G., Taylor G.I., The penetration of fluid into a porous medium Hele-Shaw cell, Proc. Roy. Soc. A 245 (1958) 312-329. | MR | Zbl

[23] J.L. Vázquez, A new look at the zero specific heat limit of the Stefan problem, Preprint, 1998.