Self-similarity in a thin film Muskat problem

Philippe Laurencot; Bogdan-Vasile Matioc

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arXiv · 1409.7329

Self-similarity in a thin film Muskat problem

Philippe Laurencot·Bogdan-Vasile Matioc

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Abstract

The large time behavior of non-negative weak solutions to a thin film approximation of the two-phase Muskat problem is studied. A classification of self-similar solutions is first provided: there is always a unique even self-similar solution while a continuum of non-symmetric self-similar solutions exist for certain fluid configurations. Despite this non-uniqueness, convergence of all non-negative weak solutions towards a self-similar solution is proved.

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Philippe Laurencot, Bogdan-Vasile Matioc. 2014-09-25. Self-similarity in a thin film Muskat problem. https://arxiv.org/abs/1409.7329

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