Moving interfaces–and in the stationary case, free boundaries–are ubiquitous in our
environment and daily life. They are at the basis of many physical, chemical, and also …

Curvature driven surface evolution plays an important role in geometry, applied mathematics
and in the natural sciences. In this paper geometric evolution equations such as mean …

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 …

Growth in the Muskat problem Page 1 Math. Model. Nat. Phenom. 15 (2020) 7 Mathematical
Modelling of Natural Phenomena https://doi.org/10.1051/mmnp/2019021 www.mmnp-journal.org …

We show existence and uniqueness of classical solutions for the motion of immersed
hypersurfaces driven by surface diffusion. If the initial surface is embedded and close to a …

THE VOLUME PRESERVING MEAN CURVATURE FLOW NEAR SPHERES 1. Introduction
Let G be a compact, closed, connected, embedded hypersurf Page 1 PROCEEDINGS OF THE …

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 …

We study the dynamics of the interface between two incompressible fluids in a two-
dimensional porous medium whose flow is modeled by the Muskat equations. For the two …

We provide existence of a unique smooth solution for a class of one-and two-phase Stefan
problems with Gibbs-Thomson correction in arbitrary space dimensions. In addition, it is …

The Willmore flow leads to a quasilinear evolution equation of fourth order. We study
existence, uniqueness and regularity of solutions. Moreover, we prove that solutions exist …