{"id":156,"date":"2021-05-12T18:04:45","date_gmt":"2021-05-12T18:04:45","guid":{"rendered":"http:\/\/silicio.math.unifi.it\/wordpress\/FIPISI\/?page_id=156"},"modified":"2021-05-31T16:36:07","modified_gmt":"2021-05-31T16:36:07","slug":"programma-quarto-incontro-2021","status":"publish","type":"page","link":"https:\/\/silicio.math.unifi.it\/wordpress\/FIPISI\/programma-quarto-incontro-2021\/","title":{"rendered":"Programma (quarto incontro 2021)"},"content":{"rendered":"

Incontri di Analisi Matematica
\ntra Firenze, Pisa e Siena<\/h1>\n

MathAnalysis(at)UniFIPISI, IV<\/h2>\n

venerd\u00ec 4 giugno 2021
\nUniversit\u00e0 di Firenze
\nStreaming<\/h3>\n

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

PROGRAMMA<\/h3>\n

14:25 apertura
\n14:30\u00a0<\/em>Francesca Carlotta Chittaro<\/strong> (Universit\u00e9 de Toulon, FR): Hamiltonian approach to sufficient optimality conditions<\/em>
\n15:25\u00a0<\/em>Matteo Franca\u00a0<\/strong>(Universit\u00e0 di Bologna):<\/em>\u00a0Stability and separation properties of Ground States for reaction-diffusion equations<\/em>
\n<\/em>16:20 pausa
\n<\/em>16:30\u00a0Nicola Visciglia\u00a0<\/strong>(Universit\u00e0 di Pisa): On the\u00a0Nonlinear Schroedinger Equation with multiplicative white noise<\/em>
\n17:25 chiusura<\/em><\/p>\n

ABSTRACT<\/p>\n

\n
\n
\n
\n
Francesca Carlotta Chittaro<\/strong>: Hamiltonian approach to sufficient optimality conditions<\/em><\/div>\n
<\/div>\n
The celebrated Pontryagin Maximum Principle (PMP) provides a (first order) necessary condition for the optimality of trajectories of optimal control problems. In most cases, however, a trajectory satisfying PMP is not optimal. For these reasons, additional optimality conditions are required.<\/div>\n
In this context, Hamiltonian methods are quite effective in establishing sufficient optimality conditions. In this talk, after a brief review of the main ideas of the general method, we will focus on optimal control problems associated with control-affine dynamics and costs of the form<\/div>\n
\\[\\int_0^T |u(t)\\varphi(x(t))|dt.\\]<\/div>\n
These kind of cost are very common in problems modeling neurobiology, mechanics and fuel-consumption.<\/div>\n
This is a joint work with L. Poggiolini (DIMAI).<\/div>\n

Matteo Franca:\u00a0<\/strong>Stability and separation properties of Ground States for reaction-diffusion equations<\/em><\/p>\n

In this talk we consider the long time behavior of positive solutions of the following Cauchy problem:<\/div>\n

$$ \\left\\{ \\begin{array}{l}
\nu_t=\\Delta u + u^{q}\\\\
\nu(0,x)= \\phi(x)\\,,
\n\\end{array} \\right. \u00a0$$
\nwhere $u :\\mathbb{R} \\times \\mathbb{R}^{n} \\to \\mathbb{R}$, $q> \\frac{n}{n-2}$ and of its generalization to spatial dependent \u00a0potentials.<\/p>\n

This equation can be regarded as a model for an exothermic reaction which may produce an explosion ($u$ is the temperature).
\nHence we have two main expected behaviors: if “$\\phi$ is large” $u$ blows up in finite time, while if “$\\phi$ is small”
\n$u$ converges to $0$ for $t$ large. Our aim is to explore the threshold between these two behaviors.<\/div>\n
In this context a key role is played by radial stationary solutions, i.e. Ground States, both regular and singular, and in particular by their separation properties.
\nIn fact, roughly speaking, they determine the threshold between blowing up and fading solutions, and if suitable ordering properties are satisfied they gain some stability.<\/div>\n
If there will be time we will discuss some recent results concerning separation properties of the stationary problem where the Laplace operator is replaced by its $p$-Laplace generalization.<\/div>\n
<\/div>\n
Nicola Visciglia:\u00a0<\/strong>On the\u00a0Nonlinear Schroedinger Equation with multiplicative white noise<\/em><\/div>\n
We prove global existence, uniqueness and convergence almost surely of solutions to a family of properly regularized and renormalized approximating equations to the Nonlinear Schroedinger Equation. One of the difficulties is connected with the low regularity of the white noise\u00a0potential,\u00a0that does not allow the use of\u00a0the standard definition of product between functions.<\/div>\n
We show how this problem can be settled by using a suitable renormalization argument,\u00a0once we exploit\u00a0a transformation first\u00a0introduced by Hairer in the context of the heat equation.\u00a0Next we show how the use of\u00a0suitable energies\u00a0allow to extend the\u00a0solutions for every time almost surely w.r.t. to the probabilistic parameter defining the white noise potential.<\/div>\n
In particular\u00a0we extend a previous result by A. Debussche and H. Weber available in the case of a\u00a0cubic Nonlinearity.<\/div>\n
This is a joint work with N. Tzvetkov.<\/div>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Incontri di Analisi Matematica tra Firenze, Pisa e Siena MathAnalysis(at)UniFIPISI, IV venerd\u00ec 4 giugno 2021 Universit\u00e0 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\u00a0Francesca Carlotta Chittaro (Universit\u00e9 de Toulon, FR): … <\/p>\n

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