Codice  QDD 96 
Titolo  Behaviour near extinction for the Fast Diffusion Equation on bounded domains 
Data  20110506 
Autore/i  Bonforte, M.; Grillo, G.; Vazquez, J.L. 
Link  Download full text  Pubblicato  Journal de Mathematiques Pures et Appliquees 
Abstract  We consider the Fast Diffusion Equation posed in a bounded smooth domain with homogeneous Dirichlet
conditions. It is known that for in a certain range of the parameter m appearing in the equation all bounded positive solutions of such problem extinguish in a finite time, and also that such solutions approach a separate variable solution. Here, we are interested in describing the behaviour of the solutions near the extinction time. We first show that the convergence takes place uniformly in the relative error norm. Then, we study the question of rates of convergence. For m close to 1 we get such rates by means of entropy methods and weighted PoincarĂ¨ inequalities. The analysis of the latter point makes an essential use of fine properties of a associated stationary elliptic problem, which has an independent interest. 
