Details
| Original language | English |
|---|---|
| Pages (from-to) | 3951-3963 |
| Number of pages | 13 |
| Journal | Nonlinear Analysis, Theory, Methods and Applications |
| Volume | 75 |
| Issue number | 10 |
| Publication status | Published - Jun 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.
Keywords
- Blow-up, Classical solution, Maximal solution, Moving boundary problem
ASJC Scopus subject areas
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 75, No. 10, 06.2012, p. 3951-3963.
Research output: Contribution to journal › Article › Research › 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 -