Mathematical models of some diffusive processes whith free boundaries

On the convexity of some free boundaries

We demonstrate that a method of Colesanti and Salani, which compares solutions of elliptic differential equations to their quasiconcave envelopes, can be extended to derive convexity of free boundaries. As examples we present the so-called dam problem, a free boundary problem modelling pollution and a Bernoulli problem. Moreover we prove strict convexity of the wet region in the dam problem in ...

Mathematical Models and Control of Catastrophic Processes

A mathematical model for spaghetti cooking with free boundaries

We propose a mathematical model for the process of dry pasta cooking with specific reference to spaghetti. Pasta cooking is a two-stage process: water penetration followed by starch gelatinization. Differently from the approach adopted so far in the technical literature, our model includes free boundaries: the water penetration front and the gelatinization onset front representing a fast stage ...

Internal null stabilization for some diffusive models of population dynamics

We investigate the large-time behavior of the solutions to some Fisher-type models with nonlocal terms describing the dynamics of biological populations with diffusion, logistic term and migration. Two types of logistic terms are taken into account. A necessary condition and a sufficient condition for the internal null stabilizability of the solution to a Fisher model with nonlocal term are pro...

Computation of Parameters in some Mathematical Models

In computational science it is common to describe dynamic systems by mathematical models in forms of differential or integral equations. These models may contain parameters that have to be computed for the model to be complete. For the special type of ordinary differential equations studied in this thesis, the resulting parameter estimation problem is a separable nonlinear least squares problem...