We discuss the dynamical behavior of the semiflow associated to the nonlinear heat equation ut − ∆u = f(x, u) on a bounded domain with Dirichlet boundary conditions. The nonlinearity f grows superline...
We consider travelling waves in spatially recurrent diffusive media, including the almost periodic and quasi-periodic ones as special cases. We first define the notion of travelling waves under such h...
We study the asymptotic behaviour near the boundary of explosive solutions of a viscous Hamilton-Jacobi equation. This model was introduced by J.M. Lasry and P.L. Lions from a state constrained proble...
Lo scopo del seminario e di presentare alcuni recenti risultati riguardanti le soluzioni dell’equazione di Lane-Emden in domini non limitati dello spazio euclideo ad N dimensioni. In particolare, si p...
I will begin by giving a survey of some known methods for a-priori bounds of positive solutions of semilinear elliptic equations on smooth bounded domains with zero Dirichlet boundary conditions. I wi...
I will discuss some recent results on the existence of multiple solutions to equations of the form −∆u = f(x, u), where the nonlinearity f has subcritical or critical growth. In some cases we find sig...
Si considera il problema di rimuovere una fissata quantita di materiale da una regione D nella maniera piu efficiente possibile. Per tener conto del fatto che non tutte le direzioni si percorrono con ...
I will discuss various modes of degeneration of differential operators and associated Lie algebras of vector fields and indicate a systematic approach to uniform invertibility under appropriate ellipt...
We introduce and analyse a general -and remarkably encompassing- concept of self (and antiself) dual partial differential equations. The class contains many of the basic families of linear and nonline...
Discuterò alcuni risultati e problemi aperti relativi alla classificazione dei solitoni compatti del flusso di Ricci. Questi sono una classe particolare di varieta riemanniane che generalizzano le var...
