Organizers: Giovanni Catino and Fabio Cipriani
Hao Wu, Fudan University, Shanghai,
Well-posedness and long-time behavior of the Hele-Shaw-Cahn-Hilliard system, Friday, April 13, 2012, time 14:00 o'clock, Aula seminari III piano
Abstract:Abstract:
The Hele-Shaw-Cahn-Hilliard model is one of the most popular system describing two-phase flows in porous media or Hele-Shaw cell using the phase-field approach. We will discuss the well-posedness and long-time behavior of the incompressible Hele-Shaw-Cahn-Hilliard system in two and three spatial dimensions. We show the convergence of global weak/strong solution to equilibrium as time goes to infinity with a rate via the Lojasiewicw-Simon technique. Stability of the energy minimizers is also discussed.
Jean Dolbeault, Universite Paris Dauphine,
Free energies, nonlinear flows and functional inequalities, Friday, Febraury 17, 2012, time 14:00 o'clock, Aula Seminari III piano
Abstract:Abstract:
This lecture will primarily be devoted to a review of results based on entropy methods in nonlinear diffusion equations. The basic example is the fast diffusion equation in the euclidean space and the study of the asymptotic behaviour of the solutions in self-similar variables. Recent results (in collaboration with G. Toscani) provide interesting refinements for the study of the asymptotic behaviour of the solutions, based on best matching asymptotic profiles rather than on self-similar rescalings. As a consequence, improved Sobolev inequalities have been obtained, thus giving an answer to an old open question raised by H. Brezis and E. Lieb. Nonlocal improvements of standard functional inequalities will also be introduced, based on duality and nonlinear flows approaches. They are connected with mean field models like the Keller-Segel system.
Giovanni Catino, Politecnico di Milano,
On the classification of some Einstein-like metrics, Friday, Febraury 03, 2012, time 14:00 o'clock, Aula Seminari III piano
Abstract:Abstract:
In this talk, I will discuss some recent results concerning the classification of some Einstein-like structure, such as Ricci solitons, Yamabe solitons
and Einstein solitons. These are special Riemannian manifolds which arise naturally as self similar solutions to some geometric flows and have been
studied intensively in recent years.
Shuai Lu, Fudan University, Shanghai, China,
On the Inverse Problems for the Coupled Continuum Pipe Flow model for flows in karst aquifers, Tuesday, December 06, 2011, time 11:30, Aula seminari III piano
Abstract:Abstract:
We investigate two inverse problems for the coupled continuum pipe flow (CCPF) model which describes the fluid flows in karst aquifers. After generalizing the well-posedness of the forward problem to the anisotropic exchange rate case which is a
space-dependent variable, we present the uniqueness of this parameter by measuring the Cauchy data. Besides, the uniqueness of the geometry of the conduit by the Cauchy data is verified as well. These results enhance the practicality of the CCPF model.
Eduardo Teixeira, Universidade Federal do Ceara, Brazil,
Nonvariational singular elliptic equations and their geometries, Friday, November 18, 2011, time 14:00 o'clock, Aula seminari VI piano
Abstract:Abstract:
In this talk I will discuss fine geometric properties of
solutions to fully nonlinear elliptic equations with singular
potentials. Singularities occurs along the (unkown) free surface {u=0}
and the degree of the singularity determines optimal regularity
estimates for u though the singular level set. These classes of
equations are related to important free boundary problems that were
previously accessed only through variational considerations.
