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…
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…
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…
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…