On the blow up scenario for a class of parabolic moving boundary problems |
| |
Authors: | Matthias Bergner Joachim Escher Friedrich-Matthias Lippoth |
| |
Institution: | 1. Institute of Differential Geometry, Leibniz University of Hanover, Welfengarten 1, D-30167, Germany;2. Institute of Applied Mathematics, Leibniz University of Hanover, Welfengarten 1, D-30167, Germany |
| |
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,α can be regarded as a graph over an analytic hypersurface, provided k≥2. |
| |
Keywords: | Moving boundary problem Blow-up Classical solution Maximal solution |
本文献已被 ScienceDirect 等数据库收录! |
|