Le proposte di nuovi seminari vanno inviate al Prof. Sandro Coriasco - sandro.coriasco[AT]unito.it o alla Prof.ssa Vivina Barutello - vivina.barutello[AT]unito.it 

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Stampa

SEMINARI DI ANALISI MATEMATICA

Evento 

Titolo:
Geometric aspects and asymptotic analysis in phase separation of coupled elliptic equations
Quando:
11.11.2015 13.30 h
Dove:
Palazzo Campana - Torino
Aula:
Aula C
Relatore:
Dott. Alessandro Zilio
Afferenza:
École des Hautes Études en Science sociales, Paris
Proponente:
S. Terracini
Locandina:
Locandina

Descrizione

We consider a family of positive solutions to the system of \(k\) components \[ -\Delta u_{i,\beta} = f(x, u_{i,\beta}) - \beta u_{i,\beta} \sum_{j \neq i} a_{ij} u_{j,\beta}^2 \qquad \text{in $\Omega$}, \] where \(\Omega \subset \mathbb{R}^N\) with \(N \ge 2\). It is known that uniform bounds in $L^\infty$ of $\{\mathbf{u}_{\beta}\}$ imply convergence of the densities to a segregated configuration, as the competition parameter $\beta$ diverges to $+\infty$. In this talk I will discuss how to obtain sharp quantitative point-wise estimates for the densities around the interface between different components, and how to characterize the asymptotic profile of $\mf{u}_\beta$ in terms of entire solutions to the limit system \[ \Delta U_i = U_i \sum_{j\neq i} a_{ij} U_j^2. \] This results can be then used in order to establish a uniform-in-$\beta$ regularity theory for the interfaces. These results are part of an ongoing project with Nicola Soave. 

Sede

Mappa
Sede:
Palazzo Campana   -   Sito web
Via:
Via Carlo Alberto, 10
Cap:
10123
Città:
Torino
Provincia:
To
Paese:
Paese: it

Descrizione

Dipartimento di Matematica, Università degli Studi di Torino

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