# Incontri di Analisi Matematica

tra Firenze, Pisa e Siena

## MathAnalysis(at)UniFIPISI, IV

### venerdì 4 giugno 2021

Università di Firenze

Streaming

Invitiamo gli interessati a compilare il modulo di registrazione. Gli utenti registrati riceveranno le informazioni per accedere alla piattaforma informatica per seguire i seminari da remoto.

### PROGRAMMA

*14:25 apertura
14:30 *

**Francesca Carlotta Chittaro**

*(Université de Toulon, FR): Hamiltonian approach to sufficient optimality conditions*

15:25

15:25

**Matteo Franca**

*(Università di Bologna):*

*Stability and separation properties of Ground States for reaction-diffusion equations*

*16:20 pausa*

16:30

**Nicola Visciglia**

*(Università di Pisa): On the Nonlinear Schroedinger Equation with multiplicative white noise*

17:25 chiusura

17:25 chiusura

ABSTRACT

**Francesca Carlotta Chittaro**:

*Hamiltonian approach to sufficient optimality conditions*

**Matteo Franca: ***Stability and separation properties of Ground States for reaction-diffusion equations*

$$ \left\{ \begin{array}{l}

u_t=\Delta u + u^{q}\\

u(0,x)= \phi(x)\,,

\end{array} \right. $$

where $u :\mathbb{R} \times \mathbb{R}^{n} \to \mathbb{R}$, $q> \frac{n}{n-2}$ and of its generalization to spatial dependent potentials.

Hence we have two main expected behaviors: if “$\phi$ is large” $u$ blows up in finite time, while if “$\phi$ is small”

$u$ converges to $0$ for $t$ large. Our aim is to explore the threshold between these two behaviors.

In fact, roughly speaking, they determine the threshold between blowing up and fading solutions, and if suitable ordering properties are satisfied they gain some stability.

**Nicola Visciglia:**

*On the Nonlinear Schroedinger Equation with multiplicative white noise*