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Volumn 14, Issue 2, 2012, Pages 267-277

Modelling and analysis of the muskat problem for thin fluid layers

Author keywords

Degenerate parabolic equations; Linearised stability; Muskat problem; Thin layers

Indexed keywords

CLASSICAL EQUATION; DEGENERATE PARABOLIC EQUATION; EXPONENTIALLY STABLE; LAYER THICKNESS; LOCAL WELL-POSEDNESS; MUSKAT PROBLEM; POROUS MEDIUM; STEADY STATE; SURFACE TENSION FORCE; THIN FLUID FILMS; THIN FLUIDS; THIN LAYERS;

EID: 79960623276     PISSN: 14226928     EISSN: 14226952     Source Type: Journal    
DOI: 10.1007/s00021-011-0053-2     Document Type: Article
Times cited : (36)

References (18)
  • 2
    • 0001835099 scopus 로고
    • Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems
    • In: Schmeisser, H., Triebel, H. (eds.) Teubner-Texte zur Math. Teubner, Stuttgart, Leipzig
    • Amann, H.: Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems. In: Schmeisser, H., Triebel, H. (eds.) Function spaces, differential operators and nonlinear analysis, Teubner-Texte zur Math. vol. 133, pp. 9- 126. Teubner, Stuttgart, Leipzig (1993)
    • (1993) Function Spaces, Differential Operators and Nonlinear Analysis , vol.133 , pp. 9-126
    • Amann, H.1
  • 3
    • 67650500731 scopus 로고    scopus 로고
    • The Rayleigh-Taylor condition for the evolution of irrotational fluid interfaces
    • Córdoba, A., Córdoba, D., Gancedo, F.: The Rayleigh-Taylor condition for the evolution of irrotational fluid interfaces. Proc. Natl. Acad. Sci. USA 106(27), 10955-10959 (2009)
    • (2009) Proc. Natl. Acad. Sci. USA , vol.106 , Issue.27 , pp. 10955-10959
    • Córdoba, A.1    Córdoba, D.2    Gancedo, F.3
  • 4
    • 34249881893 scopus 로고    scopus 로고
    • Contour dynamics of incompressible 3-D fluids in a porous medium with different densities
    • Córdoba, D., Gancedo, F.: Contour dynamics of incompressible 3-D fluids in a porous medium with different densities. Commun. Math. Phys. 273, 445-471 (2007)
    • (2007) Commun. Math. Phys. , vol.273 , pp. 445-471
    • Córdoba, D.1    Gancedo, F.2
  • 6
    • 84856449541 scopus 로고    scopus 로고
    • Thin Film Equations with soluble surfactant and gravity: Modeling and stability of steady states
    • arXiv:1002.1785v1 (to appear
    • Escher, J., Hillairet, M., Laurençot, P., Walker C.: Thin film equations with soluble surfactant and gravity: Modeling and stability of steady states. Math. Nachr. arXiv:1002.1785v1 (to appear)
    • Math. Nachr
    • Escher, J.1    Hillairet, M.2    Laurençot, P.3    Walker, C.4
  • 8
    • 79953645127 scopus 로고    scopus 로고
    • On the parabolicity of the Muskat problem: Well-posedness, fingering, and stability results
    • Escher, J., Matioc, B.-V.: On the parabolicity of the Muskat problem: Well-posedness, fingering, and stability results. Z. Anal. Anwend, (2011)
    • (2011) Z. Anal. Anwend
    • Escher, J.1    Matioc, B.-V.2
  • 10
    • 0037379124 scopus 로고    scopus 로고
    • Nonlinear stability of the Muskat problem with capillary pressure at the free boundary
    • Friedman, A., Tao, Y.: Nonlinear stability of the Muskat problem with capillary pressure at the free boundary.. Nonlinear Anal. 53, 45-80 (2003)
    • (2003) Nonlinear Anal. , vol.53 , pp. 45-80
    • Friedman, A.1    Tao, Y.2
  • 11
    • 52049122591 scopus 로고    scopus 로고
    • A justification for the thin film approximation of Stokes flow with surface tension
    • Günther, M., Prokert, G.: A justification for the thin film approximation of Stokes flow with surface tension. J. Differ. Equ. 245, 28002-28045 (2008)
    • (2008) J. Differ. Equ. , vol.245 , pp. 28002-28045
    • Günther, M.1    Prokert, G.2
  • 13
    • 0041033033 scopus 로고
    • Two fluid systems in porous media. The encroachment of water into an oil sand
    • Muskat, M.: Two fluid systems in porous media. The encroachment of water into an oil sand. Physics 5, 250-264 (1934)
    • (1934) Physics , vol.5 , pp. 250-264
    • Muskat, M.1
  • 14
    • 0002418219 scopus 로고
    • The instability of liquid surfaces when accelerated in a direction perpendicular to their planes
    • Taylor, G.: The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. Proc. R. Soc. Lond. Ser. A 201, 192-196 (1950)
    • (1950) Proc. R. Soc. Lond. Ser. A , vol.201 , pp. 192-196
    • Taylor, G.1
  • 15
    • 0001383598 scopus 로고
    • The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous fluid
    • Saffman, P.G., Taylor, G.I.: The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous fluid. Proc. R. Soc. Lond. Ser. A 245, 312-329 (1958)
    • (1958) Proc. R. Soc. Lond. Ser. A , vol.245 , pp. 312-329
    • Saffman, P.G.1    Taylor, G.I.2
  • 16
    • 4544228729 scopus 로고    scopus 로고
    • Global existence, singular solutions, and Ill-Posedness for the Muskat Problem
    • Siegel, M., Caflisch, R.E., Howison, S.: Global Existence, Singular Solutions, and Ill-Posedness for the Muskat Problem. Commun. Pure Appl. Math. 57, 1374-1411 (2004)
    • (2004) Commun. Pure Appl. Math. , vol.57 , pp. 1374-1411
    • Siegel, M.1    Caflisch, R.E.2    Howison, S.3
  • 18
    • 0348015444 scopus 로고    scopus 로고
    • Local classical solution of Muskat free boundary problem
    • Yi, F.: Local classical solution of Muskat free boundary problem. J. Partial Differ. Equ. 9, 84-96 (1996)
    • (1996) J. Partial Differ. Equ. , vol.9 , pp. 84-96
    • Yi, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.