Large solutions for nonlinear parabolic equations without absorption terms

In this paper we give a suitable notion of entropy solution of parabolic p-laplacian type equations with 1 p <2 which blows up at the boundary of the domain. We prove existence and uniqueness of this type of solutions when the initial datum is locally integrable (for 1 < p <2) or integrable (for p = 1; i.e. the total variation flow case). © 2011 Elsevier Inc. All rights reserved