Some Infinite Free Boundary Problems

A direct algorithm in some free boundary problems

In this paper we propose a new algorithm for the well known elliptic obstacle problem and for parabolic variational inequalities like oneand two-phase Stefan problem and of obstacle type. Our approach enters the category of xed domain methods and solves just linear elliptic or parabolic equations and their discretization at each iteration. We prove stability and convergence properties. The appr...

Some free boundary problems involving non-local diffusion and aggregation

We report on recent progress in the study of evolution processes involving degenerate parabolic equations which may exhibit free boundaries. The equations we have selected follow two recent trends in diffusion theory: considering anomalous diffusion with long-range effects, which leads to fractional operators or other operators involving kernels with large tails; and the combination of diffusio...

On Free Boundary Problems

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...

Boundary Control of Some Infinite Dimensional Systems

We will consider the feedback stabilization of a class of in£nite dimensional systems by using boundary control, i.e. control inputs are applied at the boundaries of such systems. Such systems usually possess an internal energy, and along their solutions a conservation of energy equation hold. By utilizing this relation, we will prove various stability results. We will also give an example on t...