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On the effect of boundaries in two-phase porous flow

PDE and Applied Math Seminar

Speaker: Rafael Granero, UC Davis
Location: 1147 MSB
Start time: Tue, Jan 28 2014, 3:10PM

During the last years the study of free boundary problems arising in fluid mechanics has gained considerable momentum. However, in the case of a confined interface, i.e., when the fluid evolves in a bounded domain, or in the case where the fluids fill a inhomogeneous medium, only few results are known.

In this talk, we will expose some results concerning the evolution of two incompressible fluids with different physical properties in a bounded and inhomogeneous porous medium. This situation is known as the inhomogeneous Muskat problem. 

We will focus on the global existence vs. finite time singularity formation and on the similarities and differences with the case where the depth is infinite and the permeability is constant. In particular we will explain a computer assisted proof of finite time singularities.