Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Linear wellposedness of the evolution equation of a mixing strip of two fluids with initially sharp interface in a porous medium

Authors: Jean Duchon and Raoul Robert
Journal: Quart. Appl. Math. 61 (2003), 723-730
MSC: Primary 76S05; Secondary 35B30, 35Q35, 76D03
DOI: https://doi.org/10.1090/qam/2019620
MathSciNet review: MR2019620
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Abstract: An illposed sharp interface equation, describing the evolution of two well separated fluids in a porous medium, is replaced by a linearly wellposed Cauchy problem for the evolution of a mixing strip described in terms of the level curves of the volume proportion of one fluid.

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  • [1] J. Duchon and R. Robert, Estimation d’opérateurs intégraux du type de Cauchy dans les échelles d’Ovsjannikov et application, Ann. Inst. Fourier (Grenoble) 36 (1986), no. 1, 83–95 (French). MR 840714
  • [2] Felix Otto, Evolution of microstructure in unstable porous media flow: a relaxational approach, Comm. Pure Appl. Math. 52 (1999), no. 7, 873–915. MR 1682800, https://doi.org/10.1002/(SICI)1097-0312(199907)52:7<873::AID-CPA5>3.3.CO;2-K
  • [3] Felix Otto, Evolution of microstructure: an example, Ergodic theory, analysis, and efficient simulation of dynamical systems, Springer, Berlin, 2001, pp. 501–522. MR 1850320
  • [4] J. Duchon and R. Robert, Sur quelques problèmes à frontière libre analytique dans le plan, Bony-Sjöstrand-Meyer seminar, 1984–1985, École Polytech., Palaiseau, 1985, pp. Exp. No. 10, 18 (French). MR 819776
  • [5] Jean Duchon and Raoul Robert, Perturbation quasi différentielle d’un semi-groupe régularisant dans une échelle d’espaces de Banach, Ann. Inst. H. Poincaré Anal. Non Linéaire 4 (1987), no. 4, 377–399 (French, with English summary). MR 917743
  • [6] Denis Serre, Systèmes de lois de conservation, Diderot éditeur, 1996
  • [7] Michael Reed and Barry Simon, Methods of modern mathematical physics. I, 2nd ed., Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York, 1980. Functional analysis. MR 751959

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DOI: https://doi.org/10.1090/qam/2019620
Article copyright: © Copyright 2003 American Mathematical Society

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