Free boundary problems in biology

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...

Concavity Properties for Free Boundary Elliptic Problems

We prove some concavity properties connected to nonlinear Bernoulli type free boundary problems. In particular, we prove a Brunn-Minkowski inequality and an Urysohn’s type inequality for the Bernoulli Constant and we study the behaviour of the free boundary with respect to the given boundary data. Moreover we prove a uniqueness result regarding the interior non-linear Bernoulli problem.

Integral Equation Methods for Free Boundary Problems∗

We outline a unified approach for treating free boundary problems arising in Finance using integral equation methods. Starting with the PDE formulations of the free boundary problems, we show how to derive nonlinear integral equations for the free boundaries in a variety of Finance applications. Methods to treat theoretical (existence, uniqueness) questions and analytical and numerical approxim...

Free Boundary Problems and Perpetual American Strangles

We consider the perpetual American strangles in the geometric jump-diffusion models. We assume further that the jump distribution is a mixture of exponential distributions. To solve the corresponding optimal stopping problem for this option, by using the approach in [5], we derive a system of equations that is equivalent to the associated free boundary problem with smooth pasting condition. We ...