Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 193-218 |
| Seitenumfang | 26 |
| Fachzeitschrift | Zeitschrift für Analysis und ihre Anwendungen |
| Jahrgang | 30 |
| Ausgabenummer | 2 |
| Publikationsstatus | Veröffentlicht - 8 Apr. 2011 |
Abstract
We study the Muskat problem in a periodic geometry and incorporate capillary as well as gravity effects in the modelling. The problem is rewritten as an abstract evolution equation. By analysing this evolution equation we prove wellposedness of the problem and we establish exponential stability of some flat equilibrium. Using bifurcation theory we also find finger shaped steady-states which are all unstable.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Angewandte Mathematik
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in: Zeitschrift für Analysis und ihre Anwendungen, Jahrgang 30, Nr. 2, 08.04.2011, S. 193-218.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - On the parabolicity of the Muskat problem
T2 - Well-Posedness, Fingering, and Stability Results
AU - Escher, Joachim
AU - Matioc, Bogdan-Vasile
PY - 2011/4/8
Y1 - 2011/4/8
N2 - We study the Muskat problem in a periodic geometry and incorporate capillary as well as gravity effects in the modelling. The problem is rewritten as an abstract evolution equation. By analysing this evolution equation we prove wellposedness of the problem and we establish exponential stability of some flat equilibrium. Using bifurcation theory we also find finger shaped steady-states which are all unstable.
AB - We study the Muskat problem in a periodic geometry and incorporate capillary as well as gravity effects in the modelling. The problem is rewritten as an abstract evolution equation. By analysing this evolution equation we prove wellposedness of the problem and we establish exponential stability of some flat equilibrium. Using bifurcation theory we also find finger shaped steady-states which are all unstable.
KW - Classical solution
KW - Stability
KW - Steady-state solutions
UR - http://www.scopus.com/inward/record.url?scp=79953645127&partnerID=8YFLogxK
U2 - 10.4171/ZAA/1431
DO - 10.4171/ZAA/1431
M3 - Article
AN - SCOPUS:79953645127
VL - 30
SP - 193
EP - 218
JO - Zeitschrift für Analysis und ihre Anwendungen
JF - Zeitschrift für Analysis und ihre Anwendungen
SN - 0232-2064
IS - 2
ER -