Asymptotic convergence of the stefan problem to hele-shaw

Transactions of the American Mathematical Society

Volumn 353, Issue 2, 2001, Pages 609-634

  Quirös, Fernando ^a   Väzquez, Juan Luis ^a  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

Asymptotic behaviour; Hele shaw; Stefan problem

Indexed keywords

EID: 23044524517     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0002-9947-00-02739-2     Document Type: Article

References (17)

1. L.A. Caffarelli, The regularity of free boundaries in higher dimensions, Acta Math. 139 (1977), 155-184. MR 56:12601
2. [CF] L.A. Caffarelli and A. Friedman, Continuity of the temperature in the Stefan problem, Indiana Univ. Math. J. 28 (1) (1979), 53-70. MR 80i:35104
3. G. Duvaut, Résolution d'un problème de Stefan (F\ision d'un bloc de glace àzéro degrés), C. R. Acad. Sei. Paris Sér. A 276 (1973), 1461-1463. MR 48:6688
4. [EJ] C.M. Elliott and V. Janovsky, A variational inequality approach to Hele-Shaw flow with a moving boundary, Proc. Royal Soc. Edinburgh 88A (1981), 93-107. MR 82d:76031
5. [F] A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, Englewood Cliffs, NJ, 1964. MR 31:6062
6. [FK] A. Friedman and D. Kinderlehrer, A one phase Stefan problem, Indiana Univ. Math. Jour. 24 (11) (1975), 1005-1035. MR 52:6190
7. [KLV] J.R. King, A.A. Lacey and J.L. Vazquez, Persistence of corners in free boundaries in Hele-Shaw flow, European Jnl. Appl. Math. 6 (1995), 445-490. MR 97a:76037
8. [KN] D. Kinderlehrer and L. Nirenberg, The smoothness of the free boundary in the one phase Stefan problem, Comm. Pure Appl. Math. 31 (1978), 257-282. MR 82b:35152
9. A.A. Lacey, Bounds on solutions of one-phase Stefan problems, European Jour. Appl. Math. 6 (1995), 509-516. MR 96j:80009
10. [LR] B. Louro and J.F. Rodrigues, Remarks on the quasi-steady one phase Stefan problem, Proc. Royal Soc. Edinburgh 102A (1986), 263-275. MR 88e:35186
11. H. Matano, Asymptotic behavior of the free boundaries arising in one phase Stefan problems in multi-dimensional spaces, in "Nonlinear Partial Differential Equations in Applied Science" (Tokyo, 1982), North-Holland Math. Stud., 81, 1983, pp. 133-151. MR 86a:35151
12. [Me] A.M. Meirmanov, The Stefan problem, Walter de Gruyter, Berlin, 1992. MR 92m:35282
13. [MGR] J.A. McGeough and H. Rasmussen, On the derivation of the quasi-steady model in electromechanical machining, 3. Inst. Math. Applies. 13 (1974), 13-21.
14. [R] S. Richardson, Hele-Shaw flows with a free boundary produced by the injection of fluid into a narrow channel, J. Fluid Mech. 56 (1972), 609-618.
15. [Ru] L.I. Rubinstein, The Stefan problem, Transi. Math. Monographs, vol. 27, Amer. Math. Soc., Providence, RI, 1971. MR50:3837
16. [ST] P.G. Saffman and G.I. Taylor, The penetration of fluid into a porous medium Hele-Shaw cell containing a more viscous liquid, Proc. Royal Soc. London Ser. A 245 (1958), 312-329. MR 20:3697
17. J.L. Vazquez, Singular solutions and asymptotic behaviour of nonlinear parabolic equations, in "International Conference on Differential Equations; Barcelona 91" (Equadiff91), (G. Perellô, C. Sirno and J. Sola-Morales eds.), World Scientific, Singapore, 1993, pp. 234-249. MR 95a:35067