Catherine Bandle, University of Basel, Sublinear elliptic problems with a Hardy potential, Thursday, May 11, 2017, time 14:15, Aula Consiglio 7° piano
Abstract:Abstract:
We discuss the existence and the boundary behavior of positive solutions of an elliptic equation with a Hardy potential and a sublinear nonlinearity. This problem has two particular features: the Hardy potential is singular at the boundary and the unique continuation property doesn’t hold. The Hardy potential forces the solutions either to vanish or to blow up at the boundary. The picture of the radial solutions in balls and annuli is fairly complete. At the end we present results for general domains and point out some open problems.

Jean-Christophe Pesquet, University Saclay, Proximity operator computation for large scale problems, Tuesday, April 11, 2017, time 15:00 o'clock, Aula seminari 3° piano
Abstract:Abstract:
Proximal methods have gained much interest for solving large-scale possibly non smooth optimization problems. When dealing with complicated convex functions, the expression of the proximity operator is however often non explicit and it thus needs to be determined numerically. We show in this work how block-coordinate algorithms can be designed to perform this task. We deduce also distributed optimization strategies allowing us to implement our solutions on multicore architectures. Applications of these methods to video restoration of old TV sequences illustrate the good performance of the proposed algorithms.

Filippo Dell'Oro, Politecnico di Milano, Asymptotic analysis of linear Moore-Gibson-Thompson equations, Wednesday, March 29, 2017, time 15:15 o'clock, Aula seminari 3° piano
Abstract:Abstract:
We consider the linear third-order Moore-Gibson-Thompson equation arising in acoustics, together with its memory relaxation. We analyze the stability properties of the solutions in dependence of the structural parameters of the models, and we discuss some intrinsic connections with the equation of linear viscoelasticity

Matteo Bonforte, Universidad Autonoma de Madrid, Nonlinear and Nonlocal Degenerate Diffusions on Bounded Domains, Thursday, March 16, 2017, time 11:00 o'clock, Aula seminari 3° piano
Abstract:Abstract:
We investigate quantitative properties of nonnegative solutions to a nonlinear fractional diffusion equation, of degenerate type, posed in a bounded domains, with appropriate homogeneous Dirichlet boundary conditions. The diffusion is driven by a quite general class of linear operators that includes the three most common versions of the fractional Laplacian in a bounded domain with zero Dirichlet boundary conditions; many other examples are included. The nonlinearity is assumed to be increasing and is allowed to be degenerate, the prototype being convex powers. We will present some recent results about existence, uniqueness and a priori estimates for a quite large class of very weak solutions, that we call weak dual solutions. We will devote special attention to the regularity theory: decay and positivity, boundary behavior, Harnack inequalities, interior and boundary regularity, and asymptotic behavior. All this is done in a quantitative way, based on sharp a priori estimates. Although our focus is on the fractional models, our techniques cover also the local case, and provide new results even in this setting. A surprising instance of this problem is the possible presence of nonmatching powers for the sharp upper and lower boundary behavior. This unexpected phenomenon is a completely new feature of the nonlocal nonlinear structure of this model, and it is not present in the elliptic case. The above results are contained on a series of recent papers in collaboration with A. Figalli, Y. Sire, X. Ros-Oton and J. L. Vazquez.

Andrzej Zuk , C.N.R.S. France et Université Paris 7, Spectra, automata and discrete analogues of the KdV equation, Monday, March 13, 2017, time 11:30 o'clock, Aula seminari 6° piano
Abstract:Abstract:
Box-Ball systems are discrete analogues of the KdV equation. We prove that their evolution can be described by automata. With these automata we associate self-adjoint operators. We relate spectral properties of these operators with L^2 Betti numbers of closed manifolds.

Genni Fragnelli, Università degli Studi di Bari, Null controllability in degenerate and singular parabolic problems, Wednesday, March 08, 2017, time 15:00 o'clock, Aula seminari 6° piano
Abstract:Abstract:
In this talk we will present the problem of null controllability for parabolic systems and we will focus on some recent results for degenerate and singular problems coming from real-world models, such as Biology, Climatology, Medicine.