Gabriele Grillo, Politecnico di Torino, On the asymptotic behaviour of some solutions of the fast diffusion equation., Tuesday, December 01, 2009, time 16:15 o'clock, Aula seminari terzo piano
Abstract:Abstract:
The so-called Barenblatt profiles are known to be explicit solution to the fast diffusion equation. Such solutions play, in the study of such equation, a role similar to the one played by the Gaussian solutions when dealing with the heat equation. In this talk we shall in fact show that, in suitable senses, certain classes of solutions to the fast diffusion equation converge to the Barenblatt profiles, giving explicit rates of convergence. Such rates are related to the best constant, explicitly determined, in a suitable Hardy-Poincaré inequality. A particular case, in which such constant vanishes, shows a polynomial decay instead of an exponential one. Such behaviour is proved using a geometric interpretation of the linearized evolution, the Li-Yau theory on the heat kernel on manifolds with nonnegative Ricci curvature, some weighted Nash inequalities and, finally, an appropriate use of the parabolic Harnack inequality. This is a report of joint works with M. Bonforte, J.L. Vazquez and, in part, A. Blanchet e J. Dolbeault.

Kazuhiro Ishige, Tohoku University (Sendai, Giappone), Blow-up for a semilinear parabolic equation with large diffusion on R^N, Tuesday, November 24, 2009, time 16:15 o'clock, aula seminari III piano
Abstract:Abstract:
We study the blow-up time and the location of the blow-up set of the solution for a semilinear heat equation with large diffusive coefficient. In particular, we prove that, if the diffusive coefficient is sufficiently lar ge, then the location of the blow-up set depends on the large time behavior of the hot spots of the solutions for the heat equation. This is a joint work with Yohei Fujishima.

Wu Hao, Fudan University Shanghai e WIAS Berlin, On a semiconductor drift-diffusion-Poisson model in R3 , Wednesday, May 20, 2009, time 16:15, Sala Seminari Fausto Saleri , VI piano
Abstract:Abstract:
We study a time-dependent as well as a stationary drift-diffusion-Poisson system for semiconductors. Global existence and uniqueness of weak solution of the time-dependent problem are proven and we also prove the existence and uniqueness of the steady state. Finally, we discuss the large time asymptotics of the time-dependent problem. This is a joint work with Prof. P. Markowich and Prof. S. Zheng.

Alexander Ioffe, Department of Mathematics, The Technion, Haifa, Tame Functions and Variational Analysis , Wednesday, May 20, 2009, time 17:15, Aula seminari Fausto Saleri, 6 piano
Abstract:Abstract:
All non-trivial theorems of local variational analysis applied to generic non-differential functions (e.g. optimization problems with generic Lipschitz data) produce not very informative, often just trivial results. Fortunately, functions that usually appear in applications have some special structures (e.g. polyhedral, linear-quadratic, spline etc.). Typically such structures are particular cases of semi-algebraic (or more generally, tame) structures. The latter turn out to be perfectly compatible with basic constructions of local variational analysis which excludes any possibility for the mentioned unpleasant phenomena to happen. Moreover, in this case a number of powerful results can be proved that are not otherwise valid. The latter statements will be clarified in the talk, both in general terms and for some important classes of problems, including standard problems of mathematical programming, gradient dynamical systems and optimal control of state-linear systems.

Guy BOUCHITTE, Université de Toulon, About existence for optimal 1-rectifiable transports, Friday, May 08, 2009, time 11:00, Aula seminari Fausto Saleri, 6 piano

BORIS S. MORDUKHOVICH, Wayne State University, VARIATIONAL ANALYSIS VIA DISCRETE APPROXIMATIONS IN OPTIMAL CONTROL, Monday, May 04, 2009, time 17:00, Aula interna 3 piano
Abstract:Abstract:
In this talk we discuss recent advances in variational analysis and its applications in dynamic optimization models governed by nonconvex differential inclusions. Our approach is based on discrete approximations of differential systems and thus related to both numerical and theoretical issues in optimization and control. The main results justify stability of discrete approximations and establish necessary optimality conditions of the Euler and Hamiltonian types.