Fabio Catalano - Home page

Curriculum Vitae.  I was born on May, the 20th 1975, in Pescara, a town on the adriatic coast of Italy.
I studied in the University of L'Aquila (Italy), where I obtained my licence in Mathematics in March 1999 with first-class honours  (110/110 e Lode).
my photo moebius band

Since 2 years, I live in Bordeaux (France), where I study to obtain the Phd degree in Applied Mathematics. I work in the Institut de Mathematiques de l'Universite Bordeaux I (France).

I'm principally interested to the domain of Partial Differential Equations and, more precisely, to the hyperbolic-type problems.

My pubblications and preprints are:

1) "The Null Condition for Semilinear wave equation with variable coefficients" published on  Serdica Mathematical Journal - Academie of Sciences Bulgares , Serdica Math. J. 25 (1999), 321-340.
2) "On a model connected with the Kirchhoff Equation" Preprint Rapport Interne N. 99.019 Universite Bordeaux I,  submitted to  Journal of Mathematical Analysis and Applications  for possible pubblication.
3) "The Cauchy Problem for the Nonlinear Klein-Gordon Equation with Mass Decreasing to zero" Preprint Rapport Interne N. 01.10 Universite Bordeaux I, submitted to Differential and Integral Equation for possible pubblication.

In these works I study two important problem in the mathematical physics: the  Wave equation and the Klein-Gordon Problem.

In "Null Condition for Semilinear wave equation with variable coefficients"  I study the nonlinear Wave Equation in  $n >= 3$-space dimension. The related Cauchy problem has small initial data. The nonlinearity is quadratic near the origin and satisfies the property of Null Condition introduced by Kleinerman.
Using the generators of the Poincare' Group, I establish suitable estimates for the decay of the local solution. The energy method and the classical Von Wahl inequalities are applied to prove the global existence and uniqueness of the solution.

The second manuscript "On a model connected with Kirchhoff Equation"  is devoted to study a special problem that generalizes the  usual  Kirchhoff Equation in $n > 3$-space dimension.  The Kirchhoff  equation phisically describes a wave that propagates with variable speed.

In "The Cauchy Problem for the Nonlinear Klein-Gordon Equation with Mass decreasing to zero"  my purpose is to study the nonlinear Klein-Gordon problem in the special case when the mass associated to the field decreases to zero. Here, I work in 2-space dimension.

Some remarks on the physical  context. It is well known that a physical model is linear if the reaction is proportional to the external force.  This proportionality is described by a constant parameter. Typical examples are given by the elastic bodies.
The linear model physically holds if the external force is small. Otherwise the model is called non-linear.
In the last 40 years, the non-linear problems have been intensively studied thank to an important developpement of mathematical techniques.

The Wave Equation  describes the transversal motion of elastic bodies.
In  1-space dimension, it provides an accurate mathematical model for the motion of a streched string; in higher space dimensions, we deal with elastic membranes.
The Cauchy problem can be interpreted as follows. Studying the propagation of a wave,  we fixe its initial profile and velocity.  Mathematically, this corresponds to assume that the initial data are known at the time t= t(0).  The nonlinearity describes the contribution due to the external force.

The Klein-Gordon equation appears in the relativistic quantum mechanics. It describes the processes involving particles of spin zero. For example, it is applied to  study the action of electromagnetic fields on the mesons.

Several physical problem are appropriately described by partial differential equations that do not admit explicit solutions.  Therefore, the only possibility is to estimate the qualitative behaviour of the solution.  This is the main purpose of the mathematical physics.

Furhter  activities concerning the Phd: The teaching and the care of cultural exchanges beetween the Universities. My  Phd is based on the program "Cotutelle de These"  between the Universite Bordeaux I and the Universita' Roma II Tor Vergata (Italy).

Workshops: My main talks:
(1) University of Pisa (05-2000)
(2) University of Bordeaux (12-1999; 04-2001).

Sports: My favorites sports are the Ski, theWindsurf and the Rollerblade.
Here below I've inserted two nice photos of windsurf and ski.
 

windsurf race.....  ski world cup.....

For more informations (such as curriculum vitae-studiorum ), please contact me by e-mail at the following addresses :