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.

Hynek Kovarik, Università di Brescia, Comportamento asintotico del p-Laplaciano, Wednesday, October 16, 2013, time 14:00 o'clock, Aula seminari III piano
Abstract:Abstract:
Consideriamo il primo autovalore dell operatore dato dalla somma del p-Laplaciano e di un potenziale V in R^n. Studiamo il comportamento asintotico di questo autovalore per V che tende a zero. Mostreremo, in particolare, come lo sviluppo asintotico dipende da p e dalla dimensione dello spazio.

Carlos Escudero, Universidad Autonoma de Madrid, Existence results for a fourth order equation arising in the theory of non-equilibrium phase transitions, Wednesday, October 02, 2013, time 14:00 o'clock, aula seminari VI piano
Abstract:Abstract:
In this talk we will introduce a model that arises in the theory of non-equilibrium phase transitions, in particular in the description of self-affine surfaces. We will briefly comment on the role that this model is meant to play in this physical theory. Furthermore, we will mention some open questions of physical nature related to it. Subsequently we will start with the rigorous analysis of our model, which is a fourth order partial differential equation. We will describe our progress in building an existence theory for the full model, which is a parabolic equation, and for its stationary counterpart. For the latter case existence and multiplicity results are provided, and for the former one we will show local in time existence of the solution, that can be made global for small enough data, and cannot if these are large enough. We will show how these results fit into the physical theory, and what open questions are left for the future.