Homogenization of a Hele-Shaw problem in periodic and random media

Archive for Rational Mechanics and Analysis

Volumn 194, Issue 2, 2009, Pages 507-530

  Kim, Inwon C ^a   Mellet, Antoine ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 70349490442     PISSN: 00039527     EISSN: 14320673     Source Type: Journal    
DOI: 10.1007/s00205-008-0161-1     Document Type: Article

References (17)

1. Akcoglu M.A., Krengel U.: Ergodic theorems for superadditive processes. J. Reine Angew. Math. 323, 53-67 (1981)
2. Blank I.: Sharp results for the regularity and stability of the free boundary in the obstacle problem. Indiana Univ. Math. J. 50(3), 1077-1112 (2001)
3. Caffarelli L.A.: The obstacle problem revisited. J. Fourier Anal. Appl. 4, 383-402 (1998)
4. Caffarelli, L.A.: The Obstacle Problem. Lezioni Fermiane [Fermi Lectures]. Accademia Nazionale dei Lincei, Rome, 1998
5. Caffarelli L.A., Lee K.-A., Mellet A.: Singular limit and Homogenization for flame propagation in periodic excitable media. Arch. Rat. Mech. Ana. 172, 153-190 (2004)
6. Caffarelli L.A., Lee K.-A., Mellet A.: Homogenization and flame propagation in periodic excitable media: The asymptotic speed of propagation. Comm. Pure Appl. Math. 59, 501-525 (2006)
7. Dal Maso G., Modica L.: Nonlinear stochastic homogenization and ergodic theory. J. Reine Angew. Math. 368, 28-42 (1986)
8. Gustafsson B.: Applications of variational inequalities to a moving boundary problem for Hele Shaw flows. SIAM J. Math. Anal. 16, 279-300 (1985)
9. Elliot C.M., Janovsky V.: A variational inequality approach to Hele-Shaw flow with a moving boundary. Proc. R. Soc. Edinburgh. Sect. A. 88(1-2), 93-107 (1981)
10. Kim I.C.: Homogenization of the free boundary velocity. Arch. Rat. Mech. Anal 185, 69-103 (2007)
11. Kim, I.C.: Error estimate on homogenization of free boundary velocities, submitted
12. Kim, I.C.: Homogenization of a model problem on contact angle dynamics, to appear in Comm. PDE
13. Primicerio M.: Stefan-like problems with space-dependent latent heat. Meccanica 5, 187-190 (1970)
14. Rodrigues J.F.: Free boundary convergence in the homogenization of the one-phase Stefan problem. Trans. Am. Math. Soc. 274(1), 297-305 (1982)
15. Rodrigues, J.F.: Obstacle problems in mathematical physics, volume 134 of North-Holland Mathematics Studies., Notas de Matemática [Mathematical Notes], 114. North-Holland, Amsterdam, 1987
16. Roubíçek T.: The Stefan problem in heterogeneous media. Ann. Inst. H. Poincare Anal. Nonlineaire 6, 481-501 (1989)
17. Voeller, V.R., Swenson, J.B., Kim, W., Paola, C.: A Fixed grid Method for Moving Boundary Problems on the Earths Surface, European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2004