2014/09/25 by Philippe Laurençot, Laurencot, Philippe, Bogdan–Vasile Matioc +1
Computer Science · Engineering · Materials Science · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films #Solidification and crystal growth phenomena
paper · doi:10.48550/arxiv.1409.7329
openalex publication_date 2014/09/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.