In this paper we prove that the multidimensional Hele-Shaw problem with kinetic condition at the free boundary is the limit case of the Stefan problem with kinetic condition at the free boundary in the classical sense when the specific heat e goes to zero. The method is the use of a fixed point theorem; the key step is to construct a suitable function space in which we can get the existence and...

Small world models are networks consisting of many local links and fewer long range ‘shortcuts’. In this paper, we consider some particular instances, and rigorously investigate the distribution of their inter–point network distances. Our results are framed in terms of approximations, whose accuracy increases with the size of the network. We also give some insight into how the reduction in typi...

We combine two non-perturbative approaches, one based on the two-particle-irreducible (2PI) action, other functional renormalization group (fRG), in an effort to develop new approximations for field theoretical description of strongly coupled systems. In particular, we exploit exact 2PI relations between two-point and four-point functions order truncate infinite hierarchy equations group. The t...