We consider the facilitated exclusion process, which is a nonergodic, kinetically constrained process. show that in hydrodynamic limit, its macroscopic behavior governed by free boundary problem. The particles evolve on one-dimensional lattice according to jump rates are degenerate, since they can vanish non-trivial configurations and create distinct phases: indeed, be totally blocked (they can...

We provide perturbative estimates for the one-phase Stefan free boundary problem and obtain regularity of flat boundaries via a linearization technique in spirit elliptic counterpart established De Silva (IFB 13, 223–238, 2011).

We assume that the Stefan problem with undercooling has a classical solution until the moment of contact of free boundaries and the free boundaries have continuous velocities until the moment of contact. Under these assumptions, we construct a smooth approximation of the global solution of the Stefan problem with undercooling, which, until the contact, gives the classical solution mentioned abo...

must be profitable. But how profitable and how successful spam campaigns are has not been quantitatively measured. One reason that this has yet to have been studied is that designing a methodology for the inquiry into the strategies and success of spammers has presented a number of knotty problems for researchers. But in a bold move, CNS faculty researchers Geoffrey Voelker and Stefan Savage (p...

The Stefan problem with Gibbs-Thomson law describes solidification phenomena for pure substances. In applications the surface energy is anisotropic leading to an anisotropic Gibbs-Thomson law. We show the existence of weak solutions to the Stefan problem with anisotropic Gibbs-Thomson law using an implicit time discretization, and variational methods in an anisotropic BV setting. Our main resul...

We assume that the Stefan problem with undercooling has a classical solution until the moment of contact of free boundaries and the free boundaries have continuous velocities until the moment of contact. Under these assumptions , we construct a smooth approximation of the global solution of the Stefan problem with undercooling, which, until the contact, gives the classical solution mentioned ab...