Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)We study a parabolic equation with logarithmic nonlinearity and homogeneous Dirichlet condition in a smooth bounded domain. We firstly prove a result about existence of positive solutions with initial data in L-p-spaces, 1 < p < infinity; in order to overcome the singular logarithmic nonlinearity, among other arguments, we employ Hardy's inequality. After, the life span of the obtained solutions is studied. In particular we show a connection between global existence and solutions of the associated elliptic problem. (C) 2010 Elsevier Inc. All rights reserved.2492349365Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAPESP [2008/04737-0, 2008/01458-2]