# PDE and Geometric Analysis Seminar - Fall 2010

The seminar will be held in room B115 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm

## Seminar Schedule

date speaker title host(s)
Sept 13 Fausto Ferrari (Bologna) Misha
Sept 27 Arshak Petrosyan (Purdue) Misha
Oct 7, Thursday, 4 pm, Room: TBA. Special day, time & room. Changyou Wang (U. of Kentucky) Misha
Oct 11 Philippe LeFloch (Paris VI) Misha
Oct 29 Friday Irina Mitrea (IMA & U of Virginia) WiMaW
Nov 1 Panagiota Daskalopoulos (Columbia U) Misha
Nov 8 Maria Gualdani (UT Austin) Misha
Date TBA Mikhail Feldman (UW Madison) TBA Local speaker
Date TBA Sigurd Angenent (UW Madison) TBA Local speaker

## Abstracts

### Fausto Ferrari (Bologna)

Semilinear PDEs and some symmetry properties of stable solutions

I will deal with stable solutions of semilinear elliptic PDE's and some of their symmetry's properties. Moreover, I will introduce some weighted Poincaré inequalities obtained by combining the notion of stable solution with the definition of weak solution.

### Arshak Petrosyan (Purdue)

Nonuniqueness in a free boundary problem from combustion

We consider a parabolic free boundary problem with a fixed gradient condition which serves as a simplified model for the propagation of premixed equidiffusional flames. We give a rigorous justification of an example due to J.L. V ́azquez that the initial data in the form of two circular humps leads to the nonuniqueness of limit solutions if the supports of the humps touch at the time of their maximal expansion.

This is a joint work with Aaron Yip.

### Changyou Wang (U. of Kentucky)

Phase transition for higher dimensional wells

For a potential function $F$ that has two global minimum sets consisting of two compact connected Riemannian submanifolds in $R^k$, we consider the singular perturbation problem:

Minimizing $\int (|\nabla u|^2+\frac{1}{\epsilon2} F(u))$ under given Dirichlet boundary data.

I will discuss a recent joint work with F.H.Lin and X.B.Pan on the asymptotic, as the parameter $\epsilon$ tends to zero, in terms of the area of minimal hypersurface interfaces, the minimal connecting energy, and the energy of minimizing harmonic maps into the phase manifolds under both Dirichlet and partially free boundary data. Our results in particular addressed the static case of the so-called Keller-Rubinstein-Sternberg problem.

TBA

TBA