Stability estimates for a linearized Muskat problem

C. Magni

Rendiconti del Seminario Matematico della Università di Padova (2000)

  • Volume: 104, page 43-57
  • ISSN: 0041-8994

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Magni, C.. "Stability estimates for a linearized Muskat problem." Rendiconti del Seminario Matematico della Università di Padova 104 (2000): 43-57. <http://eudml.org/doc/108537>.

@article{Magni2000,
author = {Magni, C.},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {free boundary; stability; fingers; Muskat problem},
language = {eng},
pages = {43-57},
publisher = {Seminario Matematico of the University of Padua},
title = {Stability estimates for a linearized Muskat problem},
url = {http://eudml.org/doc/108537},
volume = {104},
year = {2000},
}

TY - JOUR
AU - Magni, C.
TI - Stability estimates for a linearized Muskat problem
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 2000
PB - Seminario Matematico of the University of Padua
VL - 104
SP - 43
EP - 57
LA - eng
KW - free boundary; stability; fingers; Muskat problem
UR - http://eudml.org/doc/108537
ER -

References

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  1. [1] F. Abergel, Well-posedness for a Cauchy problem associated to time dependent free boundaries with nonlocal leading terms, Commun. in Partial Differential Equations, 21, n. 9-10 (1996), pp. 1307-1319. Zbl0857.35139MR1410831
  2. [2] F. Abergel - J. Mossino, Characterization of the multidimensional Muskat problem and existence of smooth solutions, C. R. Acad. Sci. Paris, 319, serie I (1994), pp. 35-40. Zbl0807.76080MR1285894
  3. [3] J.S. Aronofsky, Trans. Aime, 195, 15 (1952). 
  4. [4] L. Boukrim - J. Mossino, Isoperimetric inequalities for a generalized multidimensional Muskat problem, C. R. Acad. Sci. Paris, 317, serie I (1993), pp. 392-332. Zbl0841.35131MR1235443
  5. [5] J.R. Cannon - A. Fasano, A nonlinear parabolic free boundary problem, Ann. Mat. Pura Appl., 4, n. 112 (1997), pp. 119-149. Zbl0348.35055MR460895
  6. [6] L.C. Evans, A free boundary problem: the flow of two immiscible fluids in a one-dimensional porous medium, I, Indiana University Mathematics Journal, 26, n. 5 (1997). Zbl0411.76066MR446055
  7. [7] W. Fulk - R. B. GUENTHER, A free boundary problem and an extension of Muskat's model, Acta Math., 122 (1969), pp. 273-300. Zbl0182.43102MR245253
  8. [8] L. Jiang - Z. Chien, Weak formulation of a multidimensional Muskat problem, in Proceedings of the Irsee Conference on Free Boundary Problems, Free Boundary Problems: Theory and Applications, II, K. H. Hoffmann and J. Sprekels ed., Pitman Res. Notes Math. Ser., n. 186 (1990). Zbl0723.35084
  9. [9] L. Jiang - J. Liang, The perturbarion of the interface of the two-dimensional diffraction problem and an approximating Muskat problem, J. Partial Differential Equations, 3, n. 2 (1990), pp. 85-96. Zbl0708.35095MR1057905
  10. [10] C. Magni, On the Muskat problem, Ph. D. Thesis, 1997. 
  11. [11] M. Muskat, Physics, 5, 250 (1943). 
  12. [12] M. Muskat, The flow of homogeneous fluids through porous media, Mc-Graw-Hill, New York (1973). JFM63.1368.03
  13. [13] A.E. Scheidegger, On the stability of displacement fronts in porous media: a discussion of the Muskat-Aronofsky model, Canad. J. Phys., 38 (1960), pp. 153-162. MR114453
  14. [14] A.E. Scheidegger, General theory of dispersion in porous media, J. Geophys. Res., 66 (1961), pp. 3273-3278. 
  15. [15] N.N. Verigin, Izv. Akad. Nauk. SSSR., 5 (1962), pp. 674-687. 

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