Qualitative behavior of solutions for thermodynamically consistent Stefan problems with surface tension

The qualitative behavior of a thermodynamically consistent two-phase Stefan problem with surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state manifolds. If a solution does not exhibit singularities in a sense made precise below, it is proved that it exists globally in time and its orbit is relatively compact. In addition, stability and instability of equilibria is studied. In particular, it is shown that multiple spheres of the same radius are unstable, reminiscent of the onset of Ostwald ripening.Comment: 56 pages. Expanded introduction, added references. This revised version is published in Arch. Ration. Mech. Anal. (207) (2013), 611-66

Control Problems for One-Dimensional Fluids and Reactive Fluids with Moving Interfaces

Abstract. The purpose of this paper is to expose several recent challenging control problems for mono-dimensional fluids or reactive fluids. These problems have in common the existence of a moving interface separating two spatial zones where the dynamics are rather different. All these problems are grounded on topics of engineering interest. The aim of the author is to expose the main control issues, possible solutions and to spur an interest for other future contributors. As will appear, mobile interfaces play key roles in various problems, and truly capture main phenomena at stake in the dynamics of the considered systems.