Regularity and nonuniqueness results for parabolic problems arising in some physical models, having natural growth in the gradient

In this paper we study the problem: [GRAPHICS] where Omega is a bounded regular domain in R-N, beta is a positive nondecreasing function and f, u(0) are positive functions satisfying some hypotheses of summability. Besides some regularity properties of all weak solutions, the main result is wild nonuniqueness theorem, which connects, via a change of unknown function, all weak solution of this problem with the solutions of some semilinear parabolic problems involving singular measure data with arbitrary support. (c) 2008 Elsevier Masson SAS. All rights reserved