Details
| Original language | English |
|---|---|
| Pages (from-to) | 193-218 |
| Number of pages | 26 |
| Journal | Zeitschrift für Analysis und ihre Anwendungen |
| Volume | 30 |
| Issue number | 2 |
| Publication status | Published - 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.
Keywords
- Classical solution, Stability, Steady-state solutions
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Zeitschrift für Analysis und ihre Anwendungen, Vol. 30, No. 2, 08.04.2011, p. 193-218.
Research output: Contribution to journal › Article › Research › 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 -