On Certain Degenerate One-phase Free Boundary Problems

Edge-degenerate Boundary Value Problems on Cones

We consider edge-degenerate families of pseudodiierential boundary value problems on a semi-innnite cylinder and study the behavior of their push-forwards as the cylinder is blown up to a cone near innnity. We show that the transformed symbols belong to a particularly convenient symbol class. This result has applications in the Fredholm theory of boundary value problems on manifolds with edges.

Phase-field models for free-boundary problems

Phase-field models are very attractive in view of their numerical simplicity. With only a few lines of code, one can model complex physical situations such as dendritic growth. From this point of view, they constitute very interesting tools for teaching purposes at graduate level. The main difficulty with these models is in their formulation, which incorporates the physical ingredients in a sub...

On Free Boundary Problems

Degenerate Parabolic Initial-Boundary Value Problems*

in Hilbert space and their realizations in function spaces as initial-boundary value problems for partial differential equations which may contain degenerate or singular coefficients. The Cauchy problem consists of solving (1.1) subject to the initial condition Jdu(0) = h. We are concerned with the case where the solution is given by an analytic semigroup; it is this sense in which the Canchy p...

Free Boundary Problems

Paradigmatic examples are the classical Stefan problem and more general models of phase transitions, where the free boundary is the moving interface between phases. Other examples come from problems in surface science, plastic molding and glass rolling, filtration through porous media, where free boundaries occur as fronts between saturated and unsaturated regions, and others from reaction-diff...