F. R. Guarguaglini

Fast Reaction Limit and Large Time Behavior of Solutions to a Nonlinear Model of Sulphation Phenomena

We investigate the qualitative behavior of solutions to the initial-boundary value problem on the half-line for a nonlinear system of parabolic equations, which arises to describe the evolution of the chemical reaction of sulphur dioxide with the surface of calcium carbonate stones. We show that, both in the fast reaction limit and for large times, the solutions of this problem are well described in terms of the solutions to a suitable one phase Stefan problem on the same domain.

GLOBAL SMOOTH SOLUTIONS FOR A HYPERBOLIC CHEMOTAXIS MODEL ON A NETWORK

In this paper we study a semilinear hyperbolic-parabolic system modeling biological phenomena evolving on a network composed of oriented arcs. We prove the existence of global (in time) smooth solutions to this problem. The result is obtained by using energy estimates with suitable transmission conditions at nodes.

Nonlinear transmission problems for quasilinear diffusion systems

We study degenerate quasilinear parabolic systems in two different domains, which are connected by a nonlinear transmission condition at their interface. For a large class of models, including those modeling pollution aggression on stones and chemotactic movements of bacteria, we prove global existence, uniqueness and stability of the solutions.

Visualizations for a numerical simulation of a flame diffusion model

Abstract This article deals with the analysis of results obtained by the numerical simulation of a mathematical model which describes a flame propagation process, by means of graphical tools. Supercomputing and animation play a fundamental role in this application which is suitable for a scientific visualization environment.

Stationary solutions and asymptotic behaviour for a chemotaxis hyperbolic model on a network

This paper approaches the question of existence and uniqueness of stationary solutions to a semilinear hyperbolic-parabolic system and the study of the asymptotic behaviour of global solutions. The system is a model for some biological phenomena evolving on a network composed by a finite number of nodes and oriented arcs. The transmission conditions for the unknowns, set at each inner node, are crucial features of the model.

A relaxation approximation for degenerate parabolic equations

We present a semilinear relaxation approximation by hyperbolic-parabolic equations for quasilinear, possibly degenerate, parabolic problems, in several space dimensions. We prove the convergence of the approximated solutions to an entropy solution of the parabolic equation.