Details
| Original language | English |
|---|---|
| Pages (from-to) | 267-277 |
| Number of pages | 11 |
| Journal | Journal of Mathematical Fluid Mechanics |
| Volume | 14 |
| Issue number | 2 |
| Publication status | Published - 29 Mar 2011 |
Abstract
We consider the evolution of two thin fluid films in a porous medium. Starting from the classical equations modelling the Muskat problem we pass to the limit of small layer thickness and obtain a system of two coupled and degenerate parabolic equations for the films height. In the absence of surface tension forces we prove local well-posedness of the problem and show that the steady-states are exponentially stable.
Keywords
- Degenerate parabolic equations, Linearised stability, Muskat problem, Thin layers
ASJC Scopus subject areas
- Mathematics(all)
- Mathematical Physics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Journal of Mathematical Fluid Mechanics, Vol. 14, No. 2, 29.03.2011, p. 267-277.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Modelling and Analysis of the Muskat Problem for Thin Fluid Layers
AU - Escher, Joachim
AU - Matioc, Anca Voichita
AU - Matioc, Bogdan-Vasile
PY - 2011/3/29
Y1 - 2011/3/29
N2 - We consider the evolution of two thin fluid films in a porous medium. Starting from the classical equations modelling the Muskat problem we pass to the limit of small layer thickness and obtain a system of two coupled and degenerate parabolic equations for the films height. In the absence of surface tension forces we prove local well-posedness of the problem and show that the steady-states are exponentially stable.
AB - We consider the evolution of two thin fluid films in a porous medium. Starting from the classical equations modelling the Muskat problem we pass to the limit of small layer thickness and obtain a system of two coupled and degenerate parabolic equations for the films height. In the absence of surface tension forces we prove local well-posedness of the problem and show that the steady-states are exponentially stable.
KW - Degenerate parabolic equations
KW - Linearised stability
KW - Muskat problem
KW - Thin layers
UR - http://www.scopus.com/inward/record.url?scp=79960623276&partnerID=8YFLogxK
U2 - 10.1007/s00021-011-0053-2
DO - 10.1007/s00021-011-0053-2
M3 - Article
AN - SCOPUS:79960623276
VL - 14
SP - 267
EP - 277
JO - Journal of Mathematical Fluid Mechanics
JF - Journal of Mathematical Fluid Mechanics
SN - 1422-6928
IS - 2
ER -