On the local well-posedness of the KP equations
On the localization of the vortices
Studiamo l'evoluzione temporale di un fluido bidimensionale incomprimibile non viscoso quando la vorticità iniziale è concentrata in regioni di diametro e mostriamo che la vorticità evoluta temporalmente è anche lei concentrata in piccole regioni di diametro , per qualunque . Noi chiamiamo questa proprietà "localizzazione". Come conseguenza abbiamo una connessione rigorosa tra il modello dei vortici puntiformi e l'Equazione di Eulero.
On the location of the peaks of least-energy solutions to semilinear Dirichlet problems with critical growth.
On the long range scattering for Stark Hamiltonians.
On the long time behavior of KdV type equations
In a series of recent papers, Martel and Merle solved the long-standing open problem on the existence of blow up solutions in the energy space for the critical generalized Korteweg- de Vries equation. Martel and Merle introduced new tools to study the nonlinear dynamics close to a solitary wave solution. The aim of the talk is to discuss the main ideas developed by Martel-Merle, together with a presentation of previously known closely related results.
On the long time behaviour of solutions of a class of autonomous reaction-diffusion systems.
On the long-time behaviour of a class of parabolic SPDE’s : monotonicity methods and exchange of stability
In this article we prove new results concerning the structure and the stability properties of the global attractor associated with a class of nonlinear parabolic stochastic partial differential equations driven by a standard multidimensional brownian motion. We first use monotonicity methods to prove that the random fields either stabilize exponentially rapidly with probability one around one of the two equilibrium states, or that they set out to oscillate between them. In the first case we can...
On the long-time behaviour of a class of parabolic SPDE's: monotonicity methods and exchange of stability
In this article we prove new results concerning the structure and the stability properties of the global attractor associated with a class of nonlinear parabolic stochastic partial differential equations driven by a standard multidimensional Brownian motion. We first use monotonicity methods to prove that the random fields either stabilize exponentially rapidly with probability one around one of the two equilibrium states, or that they set out to oscillate between them. In the first case we can...
On the long-time behaviour of compressible fluid flows subjected to highly oscillating external forces
We show that the global-in-time solutions to the compressible Navier-Stokes equations driven by highly oscillating external forces stabilize to globally defined (on the whole real line) solutions of the same system with the driving force given by the integral mean of oscillations. Several stability results will be obtained.
On the long-time behaviour of solutions of the p-Laplacian parabolic system
Convergence of global solutions to stationary solutions for a class of degenerate parabolic systems related to the p-Laplacian operator is proved. A similar result is obtained for a variable exponent p. In the case of p constant, the convergence is proved to be , and in the variable exponent case, L² and -weak.
On the low frequency asymptotics in electromagnetic theory.
On the low wave number behavior of two-dimensional scattering problems for an open arc.
On the lowest eigenvalue of the Laplacian for the intersection of two domains.
On the Martin compactification of a bounded Lipschitz domain in a riemannian manifold
The Martin compactification of a bounded Lipschitz domain is shown to be for a large class of uniformly elliptic second order partial differential operators on .Let be an open Riemannian manifold and let be open relatively compact, connected, with Lipschitz boundary. Then is the Martin compactification of associated with the restriction to of the Laplace-Beltrami operator on . Consequently an open Riemannian manifold has at most one compactification which is a compact Riemannian...
On the mathematical analysis and optimization of chemical vapor infiltration in materials science
On the Mathematical Analysis and Optimization of Chemical Vapor Infiltration in Materials Science
In this paper we present an analysis of the partial differential equations that describe the Chemical Vapor Infiltration (CVI) processes. The mathematical model requires at least two partial differential equations, one describing the gas phase and one corresponding to the solid phase. A key difficulty in the process is the long processing times that are typically required. We address here the issue of optimization and show that we can choose appropriate pressure and temperature to minimize these...
On the mathematical and numerical modelling of electron beams
On the mathematical and numerical study of non-viscous axially symmetric channel flows
On the mathematical basis of the linear sampling method.
On the Mathematics of EEG and MEG in Spheroidal Geometry