The nonlinear N-membranes evolution problem

The parabolic N-membranes problem for the p-Laplacian and the complete order constraint on the components of the solution are studied in what concerns the approximation, regularity, and stability of variational solutions. To the evolutionary case is extended the characterization of the Lagrange multipliers associated with the ordering constraint in terms of characteristic functions of coincidence sets. Continuous dependence results are given, and the asymptotic behavior as t∈→∈∞ of the solution and the coincidence sets, showing that they converge to their stationary counterparts, is studied. Bibliography: 22 titles. © 2009 Springer Science+Business Media, Inc.