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.

Anna L. Mazzucato, Penn State University, Analisi dello strato limite per una classe di flussi incomprimibili non lineari, Monday, June 23, 2014, time 15:00 o'clock, Aula seminari III piano
Abstract:Abstract:
Si discutono alcuni risultati recenti sull'analisi rigorosa del limite per viscosita' nulla e sullo stato limite associato per una certa classe di fluidi incomprimibili non lineari tridimensionali.

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.

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.