Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
840658 | Nonlinear Analysis: Theory, Methods & Applications | 2012 | 13 Pages |
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 Hölder regularity class ck,αck,α can be regarded as a graph over an analytic hypersurface, provided k≥2k≥2.
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Authors
Matthias Bergner, Joachim Escher, Friedrich-Matthias Lippoth,