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.
- 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
- 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, DOI https://doi.org/10.1002/%28SICI%291097-0312%28199907%2952%3A7%3C873%3A%3AAID-CPA5%3E3.3.CO%3B2-K
- Felix Otto, Evolution of microstructure: an example, Ergodic theory, analysis, and efficient simulation of dynamical systems, Springer, Berlin, 2001, pp. 501–522. MR 1850320
- 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
- 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
Denis Serre, Systèmes de lois de conservation, Diderot éditeur, 1996
- 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
Jean Duchon and Raoul Robert, Estimation d’opérateurs intégraux du type de Cauchy dans les échelles d’Ovsjannikov et application, Ann. Inst. Fourier (Grenoble) 36 (1), 83–95 (1986)
Felix Otto, Evolution of microstructure in unstable porous media flow: A relaxational approach, Comm. Pure Appl. Math. 52 (7) 873–915 (1999)
Felix Otto, Evolution of microstructure: An example, Ergodic theory, analysis, and efficient simulation of dynamical systems, Springer, Berlin, pages 501–522, 2001
Jean Duchon and Raoul Robert, Sur quelques problèmes à frontière libre analytique dans le plan, Séminaire Bony-Sjöstrand-Meyer (Ecole Polytechnique, Palaiseau), 1985
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 (4) 377–399 (1987)
Denis Serre, Systèmes de lois de conservation, Diderot éditeur, 1996
Michael Reed and Barry Simon, Methods of modern mathematical physics. I. Functional analysis, Academic Press, 1980
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© Copyright 2003
American Mathematical Society
