CodiceQDD 153
TitoloSharp asymptotics for the porous media equation in low dimensions via Gagliardo-Nirenberg inequalities
Autore/iGrillo, G.; Muratori, M.
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AbstractWe 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.