Details
| Originalsprache | Englisch |
|---|---|
| Seiten (von - bis) | 3951-3963 |
| Seitenumfang | 13 |
| Fachzeitschrift | Nonlinear Analysis, Theory, Methods and Applications |
| Jahrgang | 75 |
| Ausgabenummer | 10 |
| Publikationsstatus | Veröffentlicht - Juni 2012 |
Abstract
We consider maximally continued classical solutions of a large class of parabolic moving boundary problems. If the maximal existence time is finite, we describe the blow up mechanism: either a suitable norm of the bulk density blows up or the geometry of the interface collapses. This can also be seen as a sufficient condition for global in time existence of classical solutions. Moreover, we prove a representation theorem saying, that any closed compact connected hypersurface of Hlder regularity class c K,α can be regarded as a graph over an analytic hypersurface, provided k≥2.
ASJC Scopus Sachgebiete
- Mathematik (insg.)
- Analysis
- Mathematik (insg.)
- Angewandte Mathematik
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in: Nonlinear Analysis, Theory, Methods and Applications, Jahrgang 75, Nr. 10, 06.2012, S. 3951-3963.
Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review
}
TY - JOUR
T1 - On the blow up scenario for a class of parabolic moving boundary problems
AU - Bergner, Matthias
AU - Escher, Joachim
AU - Lippoth, Friedrich Matthias
PY - 2012/6
Y1 - 2012/6
N2 - We consider maximally continued classical solutions of a large class of parabolic moving boundary problems. If the maximal existence time is finite, we describe the blow up mechanism: either a suitable norm of the bulk density blows up or the geometry of the interface collapses. This can also be seen as a sufficient condition for global in time existence of classical solutions. Moreover, we prove a representation theorem saying, that any closed compact connected hypersurface of Hlder regularity class c K,α can be regarded as a graph over an analytic hypersurface, provided k≥2.
AB - We consider maximally continued classical solutions of a large class of parabolic moving boundary problems. If the maximal existence time is finite, we describe the blow up mechanism: either a suitable norm of the bulk density blows up or the geometry of the interface collapses. This can also be seen as a sufficient condition for global in time existence of classical solutions. Moreover, we prove a representation theorem saying, that any closed compact connected hypersurface of Hlder regularity class c K,α can be regarded as a graph over an analytic hypersurface, provided k≥2.
KW - Blow-up
KW - Classical solution
KW - Maximal solution
KW - Moving boundary problem
UR - http://www.scopus.com/inward/record.url?scp=84859701860&partnerID=8YFLogxK
U2 - 10.1016/j.na.2012.02.001
DO - 10.1016/j.na.2012.02.001
M3 - Article
AN - SCOPUS:84859701860
VL - 75
SP - 3951
EP - 3963
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
SN - 0362-546X
IS - 10
ER -