Organizers: Stefano Biagi, Filippo Dell’Oro, Filippo Giuliani.
DEBDIP GANGULY, POLITECNICO DI TORINO,
PARTIAL DIFFERENTIAL EQUATIONS ON HYPERBOLIC SPACE , Friday, November 28, 2014, time 14:30 o'clock, Aula Seminari III piano
Abstract:Abstract:
In this talk, semilinear elliptic partial differential equations(PDEs) on hy-perbolic space and related problems will be presented. Several geometric problems lead to the study of the equation:
$$- \Delta _{B ^N} u - \lambda u = |u| ^ {p-2} u , u \in H ^ 1 (B ^N)$$
where $\lambda$ is a real parameter and $H^1(B^N)$ denotes the Sobolev space on the conformal ball model of the hyperbolic space. Some existence, non existence and qualitative properties of solutions of above equation will be pointed out.
Daniele Castorina, Università di Padova,
Ground States for Diffusion Dominated Free Energies with Logarithmic Interaction, Thursday, November 27, 2014, time 12:00 o'clock, Aula seminari III piano
Abstract:Abstract:
Replacing linear diffusion by a degenerate diffusion of porous medium type is known to regularize the classical two-dimensional parabolic-elliptic Keller-Segel model as in Calvez-Carrillo JMPA2006.
The implications of nonlinear diffusion are that solutions exist globally and are uniformly bounded in time. We analyse the stationary case showing the existence of a unique, up to translation, global minimizer of the associated free energy.
Furthermore, we prove that this global minimizer is a radially decreasing compactly supported continuous density function which is smooth inside its support, and it is characterized as the unique compactly supported stationary state of the evolution model.
This unique profile is the clear candidate to describe the long time asymptotics of the diffusion dominated classical Keller-Segel model for general initial data.
This is a joint work with Josè Antonio Carrillo and Bruno Volzone.
Ederson Moreira dos Santos, Università di Sao Paulo, Brasile,
Hénon type equations and concentration on spheres , Friday, September 12, 2014, time 12:00 o'clock, Aula seminari III piano
Abstract:Abstract:
In this talk, I will present the concentration profile of various kind of symmetric solutions of some semilinear elliptic problems arising in astrophysics and in diffusion phenomena. Motivated by these elliptic equations and exploiting their symmetry, I will discuss about solutions that concentrate and blow up at points and around spheres as the concentration parameter tends to infinity.
This seminar is organized within the PRIN 2012 Research project «Equazioni alle derivate parziali di tipo ellittico e parabolico: aspetti geometrici, disuguaglianze collegate, e applicazioni - Partial Differential Equations and Related Analytic-Geometric Inequalities» Grant Registration number 2012TC7588_003, funded by MIUR – Project coordinator Prof. Filippo Gazzola
Maurizio Garrione, Università di Milano Bicocca,
Traveling waves for reaction-diffusion equations involving the curvature operator, Wednesday, July 02, 2014, time 16:00, Aula seminari III piano
Abstract:Abstract:
We are concerned with the existence of monotone traveling waves which connect two equilibria for a reaction-diffusion PDE where the spatial diffusion is of mean-curvature type. We study the set of the admissible speeds (i.e., the numbers c for which there exists a traveling wave as above with speed c) for different kinds of reaction terms, showing analogies and differences with respect to the linear diffusion case. The technique used relies on a change of variables leading to a suitable first order reduction.
Yongda Wang, Politecnico di Milano,
Blow-up and global existence results for fourth order hyperbolic equations, Wednesday, June 18, 2014, time 16:30 o'clock, Aula seminari III piano
Abstract:Abstract:
In this talk, we consider a class of fourth order hyperbolic equations, which is viewed as a mathematical model for suspension bridges. For this kind of problems, there exists a unique local solution. By the potential well theory, we show finite time blow-up and global existence results of the problems for different initial data.
