Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 567-586 |
| Seitenumfang | 20 |
| Fachzeitschrift | Journal of Evolution Equations |
| Jahrgang | 7 |
| Ausgabenummer | 3 |
| Publikationsstatus | Veröffentlicht - 16 Apr. 2007 |
Abstract
In this article, we study the motion of an incompressible homogeneous Newtonian fluid in a rigid porous medium of infinite extent. The fluid is bounded below by a fixed layer having an external source (with an injection rate b), and above by a free surface moving under the influence of gravity. The flow is governed by Darcy's law. If b(c) = 0 for some c > 0 then the system admits (u, f) ≡ (c, c) as an equilibrium solution. We shall prove that the stability properties of this equilibrium are determined by the slope of b in c : The equilibrium is unstable if b'(c) < 0, whereas b'(c) > 0 implies exponential stability.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Mathematik (sonstige)
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in: Journal of Evolution Equations, Jahrgang 7, Nr. 3, 16.04.2007, S. 567-586.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - Stabilization of flows through porous media
AU - Escher, Joachim
AU - Feng, Zhaoyong
N1 - Funding information: Mathematics Subject Classifications (2000): 35Q35. Key words: Analytic semigroups, Fourier multipliers, Little Hölder spaces, Stability of equilibria. The second author is corresponding author. He is grateful to the DFG for financial support through the Graduiertenkolleg 615 “Interaction of Modeling, Computation Methods and Software Concepts for Scientific-Technological Problems”.
PY - 2007/4/16
Y1 - 2007/4/16
N2 - In this article, we study the motion of an incompressible homogeneous Newtonian fluid in a rigid porous medium of infinite extent. The fluid is bounded below by a fixed layer having an external source (with an injection rate b), and above by a free surface moving under the influence of gravity. The flow is governed by Darcy's law. If b(c) = 0 for some c > 0 then the system admits (u, f) ≡ (c, c) as an equilibrium solution. We shall prove that the stability properties of this equilibrium are determined by the slope of b in c : The equilibrium is unstable if b'(c) < 0, whereas b'(c) > 0 implies exponential stability.
AB - In this article, we study the motion of an incompressible homogeneous Newtonian fluid in a rigid porous medium of infinite extent. The fluid is bounded below by a fixed layer having an external source (with an injection rate b), and above by a free surface moving under the influence of gravity. The flow is governed by Darcy's law. If b(c) = 0 for some c > 0 then the system admits (u, f) ≡ (c, c) as an equilibrium solution. We shall prove that the stability properties of this equilibrium are determined by the slope of b in c : The equilibrium is unstable if b'(c) < 0, whereas b'(c) > 0 implies exponential stability.
KW - Analytic semigroups
KW - Fourier multipliers
KW - Little Hölder spaces
KW - Stability of equilibria
UR - http://www.scopus.com/inward/record.url?scp=34547843501&partnerID=8YFLogxK
U2 - 10.1007/s00028-007-0316-9
DO - 10.1007/s00028-007-0316-9
M3 - Article
AN - SCOPUS:34547843501
VL - 7
SP - 567
EP - 586
JO - Journal of Evolution Equations
JF - Journal of Evolution Equations
SN - 1424-3199
IS - 3
ER -