Codice QDD 153 Titolo Sharp asymptotics for the porous media equation in low dimensions via Gagliardo-Nirenberg inequalities Data 2013-04-03 Autore/i Grillo, G.; Muratori, M. Link Download full text Abstract We prove sharp asymptotic bounds for solutions to the porous media equation with homogeneous Dirichlet or Neumann boundary conditions on a bounded Euclidean domain, in dimension one and two. This is achieved by making use of appropriate Gagliardo-Nirenberg inequalities only. The generality of the discussion allows to prove similar bounds for weighted porous media equations, provided one deals with weights for which suitable Gagliardo-Nirenberg inequalities hold true. Moreover, we show equivalence between such functional inequalities and the mentioned asymptotic bounds for solutions.