Maarten V. De Hoop, Purdue University, Spatio-temporal imaging of ruptures and the discrete-time dependent inverse source problem for the wave equation, Monday, June 09, 2014, time 15:00 o'clock, Aula seminari VI piano
Abstract:Abstract:
We first introduce and present an analysis of seismic waves starting from the system of elastic-gravitational equations describing the free oscillations of the earth. We establish an existence and uniqueness result to a weak formulation under minimal regularity assumptions. We then briefly describe the extraction of surface waves and body waves using techniques from semi-classical analysis. We finally discuss the discrete-time dependent inverse source problem and present an explicit reconstruction of microseisms and ruptures from body-wave data under certain conditions derived from local energy decay.

Hugo Tavares, Instituto Superior Tecnico, Universidade de Lisboa, Existence and regularity of solutions to optimal partition problems involving Laplacian eigenvalues, Wednesday, May 07, 2014, time 11:00 o'clock, Aula seminari III piano
Abstract:Abstract:
In this talk we consider a wide class of optimal partition problems involving Dirichlet eigenvalues of elliptic operators, with monotone cost functions. We prove the existence of an open optimal partition proving as well its regularity in the sense that the common boundary is, up to a residual set, locally a regular hypersurface. The proof involves a careful study of an associate Schrodinger system with competition terms, as well as several free boundary techniques (joint work with M. Ramos and S. Terracini).

Pelin G. Geredeli , Department of Mathematics, Hacettepe University, Ankara, On the parabolic equation with the nonlinear Laplacian , Tuesday, April 15, 2014, time 14:00 o'clock, Aula seminari III piano
Abstract:Abstract:
We consider a nonlinear evolution equation of parabolic type having the p-Laplacian as leading operator. Under very general conditions on the nonlinearity, we prove the existence of a regular global attractor. When the nonlinearity is monotone, and in absence of external source terms, we give an explicit estimate of the decay rate to zero of the solution.

Matteo Novaga, Universita di Pisa, An obstacle problem for the parabolic biharmonic equation, Friday, April 04, 2014, time 11:30 o'clock, Aula seminari III piano
Abstract:Abstract:
We discuss the regularity of solutions to the obstacle problem for the parabolic biharmonic equation. The equation is discretized via an implicit variational scheme, and we obtain regularity estimates which are uniform in the discretization. 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» Grant Registration number 2012TC7588_003, funded by MIUR - Project coordinator Prof. Filippo Gazzola

Octavio Vera Villagran, University of Bío-Bío, Smoothing properties for the high order nonlinear Schrodinger equation. , Tuesday, March 25, 2014, time 13:45, Aula Seminari III piano
Abstract:Abstract:
In this talk, we will show gain in regularity for certain nonlinear dispersive evolution equation (KdV, Coupled system KdV, Schrodinger equation, coupled system, Beney-Lin type). Finally, we show the gain of regularity for the high order nonlinear Schrodinger equation.

Pedro Antunes, Group of Mathematical Physics - University of Lisbon, Numerical shape optimization using the Method of Fundamental Solutions, Wednesday, November 06, 2013, time 14:00 o'clock, Aula seminari III piano
Abstract:Abstract:
In this talk we consider some shape optimization problems for eigenvalues of the Laplacian and Bilaplacian (clamped plate and buckled plate eigenvalue problems). The solution of these problems has been studied by using several numerical methods. We address the use of a gradient type method with the Method of Fundamental Solutions (MFS) as forward solver. The MFS is a meshless method that allows the solution of the eigenvalue problems with high accuracy, even with small dimension matrices. This feature allows to consider also the shape optimization with 3D and 4D domains. Several examples are presented to illustrate the good performance of the method.