Hele-Shaw flow in thin threads: A rigorous limit result

Matioc, Bogdan-Vasile; Prokert, Georg

Original version

Matioc, B.-V.; Prokert, G.: Hele-Shaw flow in thin threads: A rigorous limit result. In: Interfaces and Free Boundaries 14 (2012), Nr. 2, S. 205-230. DOI: https://doi.org/10.4171/IFB/280

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To cite the version in the repository, please use this identifier: https://doi.org/10.15488/2319

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Abstract:
We rigorously prove the convergence of appropriately scaled solutions of the 2D Hele-Shaw moving boundary problem with surface tension in the limit of thin threads to the solution of the formally corresponding Thin Film equation. The proof is based on scaled parabolic estimates for the nonlocal, nonlinear evolution equations that arise from these problems. © European Mathematical Society 2012.
License of this version:	Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. Dieser Beitrag ist aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich.
Publication type:	Article
Publishing status:	publishedVersion
Publication date:	2012
Keywords english:	Degenerate parabolic equation, Hele-Shaw flow, Surface tension, Thin Film equation
DDC:	510 \| Mathematik