It is shown that surface tension effects on the free boundary are regularizing for Hele-Shaw
models. This implies, in particular, existence and uniqueness of classical solutions for a …

This monograph presents recent and new ideas arising from the study of problems of planar
fluid dynamics, and which are interesting from the point of view of geometric function theory …

This article is concerned with a system of semilinear parabolic equations with a free
boundary, which arises in a predator–prey ecological model. The conditions for the …

The classical Stefan model is a free boundary problem that represents thermal processes in
phase transitions just by accounting for heat-diffusion and exchange of latent heat. The …

The Mullins–Sekerka model is a nonlocal evolution model for hypersurfaces, which arises
as a singular limit for the Cahn–Hilliard equation. We show that classical solutions exist …

We consider a system of two hyperbolic equations for p, q and two elliptic equations for c,σ,
where p, q are the densities of cells within the tumor \Omega_t in proliferating and quiescent …

We consider the Muskat problem describing the motion of two unbounded immiscible fluid
layers with equal viscosities in vertical or horizontal two-dimensional geometries. We first …

In this paper we introduce a notion of viscosity solutions for the one-phase Hele-Shaw and
Stefan problems when there is no surface tension. We prove the uniqueness and existence …

One of the most influential works in fluid dynamics at the edge of the XIXth and XXth
centuries was a series of papers, see, eg,[265], written by Henry Selby Hele-Shaw between …

In this article, we study a free boundary problem for a system of two partial differential
equations, one parabolic and other elliptic. The system models the growth of a tumor with …