@article{10902/30377,
year = {2014},
url = {https://hdl.handle.net/10902/30377},
abstract = {In this work we study the evolution of the free boundary between two different fluids in a porous medium where the permeability is a two dimensional step function. The medium can fill the whole plane R 2 or a bounded strip S D R  . =2;  =2/. The system is in the stable regime if the denser fluid is below the lighter one. First, we show local existence in Sobolev spaces by means of energy method when the system is in the stable regime. Then we prove the existence of curves such that they start in the stable regime and in finite time they reach the unstable one. This change of regime (turning) was first proven in [5] for the homogenous Muskat problem with infinite depth.},
organization = {The authors are supported by the Grants MTM2011-26696 and SEV-2011- 0087 from Ministerio de Ciencia e Innovación (MICINN). Diego Córdoba was partially supported by StG-203138CDSIF of the ERC. Rafael Granero-Belinchón is grateful to the former Department of Applied Mathematics ”Ulisse Dini” of the Pisa University for the hospitality during May–July 2012. We are grateful tInstituto de Ciencias Matemáticas (Madrid) and to the Dipartimento di Ingegneria Aerospaziale (Pisa) for computing facilities.},
publisher = {European Mathematical Society Publishing House},
publisher = {Interfaces and Free Boundaries, 2014, 16, 175-213},
title = {Local solvability and turning for the inhomogeneous Muskat problem},
author = {Berselli, Luigi C. and Córdoba, Diego and Granero Belinchón, Rafael},
}