The problem of Dirichlet for evolution one-dimensional p-Laplacian with nonlinear source

In the present paper we consider the Dirichlet problem for one-dimensional p-Laplacian with nonlinear source. We obtain new a priori estimates of a solution and of the gradient of a solution and formulate conditions guaranteeing the global solvability of this problem. Our consideration includes singular case as well. © 2007 Elsevier Inc. All rights reserved.