4 papers
Well-posedness of a Hele-Shaw problem in general dimensions
Olga Turanova, Yuming Paul Zhang
We investigate a Hele-Shaw type free boundary problem in general spatial dimension. We establish a comparison principle and well-posedness for the problem using a notion of viscosi…
The incompressible limit of an inhomogeneous model of tissue growth
Anthony Sulak, Olga Turanova
We study a porous medium equation that models tissue growth in a heterogeneous environment. We show that, in the incompressible limit, solutions converge to those of a weak form of…
A Hele-Shaw problem with interior and free boundary oscillation: well-posedness and homogenization
Olga Turanova, Yuming Paul Zhang
We investigate a Hele-Shaw type free boundary problem in one spatial dimension, where heterogeneities appear both on the free boundary and within the interior of the positivity set…
Well-posedness for viscosity solutions of the one-phase Muskat problem in all dimensions
Russell Schwab, Son Tu, Olga Turanova
In this article, we apply the viscosity solutions theory for integro-differential equations to the \emph{one-phase} Muskat equation (also known as the Hele-Shaw problem with gravit…