The nonlinear N-membranes evolution problem

Details The nonlinear N-membranes evolution problem The nonlinear N-membranes evolution problem

2008-12-09

arxiv.org/abs/0812.1646v1

Mathematics

Analysis of PDEs

16 pages

Scientific paper

The parabolic N-membranes problem for the p-Laplacian and the complete order constraint on the components of the solution is studied in what concerns the approximation, the regularity and the stability of the variational solutions. We extend to the evolutionary case the characterization of the Lagrange multipliers associated with the ordering constraint in terms of the characteristic functions of the coincidence sets. We give continuous dependence results, and study the asymptotic behavior as $t \to \infty$ of the solution and the coincidence sets, showing that they converge to their stationary counterparts.

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